A conversion factor is a mathematical expression that is used to convert a quantity from one unit of measure to another. It is a ratio that expresses the relationship between two different units of measurement.
There are many conversion factors used to convert one unit of measure to another. Here are some common conversion factors that you may find useful:
1 inch = 2.54 centimeters
1 foot = 0.3048 meters
1 mile = 1.609 kilometers
1 pound = 0.4536 kilograms
1 ounce = 28.35 grams
1 gallon = 3.785 liters
1 liter = 1000 milliliters
1 meter = 100 centimeters
1 kilometer = 1000 meters
1 square meter = 10.764 square feet
1 cubic meter = 35.315 cubic feet
1 atmosphere = 101.3 kilopascals
These are just a few examples of the many conversion factors that are used in various fields of science, engineering, and everyday life. It's important to know and use the appropriate conversion factor when converting units of measure to ensure accurate and meaningful results.
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Which four statements that are true?
y=e" and y = ln x are inverses.
are not equivalent.
In een
In(x) = log. (x)
ln e = 1
In (x) = log10 (x)
In e = 10
In(e) and en both equal x.
The statements are:
y=e" and y = ln x are inverses.
This is false. The inverse of y = e^x is y = ln x, and the inverse of y = ln x is y = e^x. So, the two functions y = e^x and y = ln x are inverses of each other, but y = e^x and y = e^ln x are not.
In een In(x) = log. (x)
This is false. The statement should be: e^ln(x) = x, which is true by the definition of logarithms.
ln e = 1
This is true. The natural logarithm of e is 1.
In (x) = log10 (x)
This is false. The statement should be: log10(x) = log(x) / log(10).
In e = 10
This is false. The natural logarithm of e is 1.
In(e) and en both equal x.
This is false. In(e) = 1, and e^n = x does not necessarily imply that In(e) = x.
Pizzazz Pizza is selling pizzas during lunch time at a festival. From 10:00 to 2:00 they served a steady stream of
customers, selling approximately 376 pizzas during the shift. Tomorrow they are also serving dinner, from 5:00 -
7:00. If sales continue at the same rate, how many pizzas will they sell TOTAL for both days?
Answer:
Step-by-step explanation:
So if they sell approximately 376 pizzas the first shift and then the same amount for the second, all you have to do is add 376 by 367 or multiply by 2 because adding the same number twice is like multiplying the number by 2.
Answer: 564
Step-by-step explanation: From 10-2 they sell 376 pizzas. So, in 4 hours they sell 376 pizzas, and they sell 94 pizzas per hour, because 376/4 is 94. So from 5-7, 2 hours, they should sell 94 times 2 pizzas, which is 188 pizzas. So 188+376 is 564.
Situation:
A geologist in South America discovers a
bird skeleton that contains 61% of its
original amount of C-14.
N = Noe-kt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
Step-by-step explanation:
Transcribed image text: Situation: Find the age of the bird skeleton to the nearest A geologist in South America discovers a bird skeleton that contains 74% of its original amount of C-14. Enter the correct answer. N-Noekt No-inital amount of C.14 (at time t 0) N amount of C-14 at time t k 0.000 t time, in years.
SOH CAH TOA TRIG RATIOS
Answer:
HI: 57.4 cm; KM: 0.4 mil
Step-by-step explanation:
Question 17:
ΔGHI is a right-angled triangle
where:
Side GI = Hypotenuse
α = 55°
With respect to 55° angle:
Side HI = Adjacent side
∴Trigonometric function used: Cosα (CAH)
Cos55° = [tex]\frac{Side HI}{100cm}[/tex]
Cross-multiplication is applied:
Side HI = (Cos55°)×(100 cm)
Side HI = 57.4 cm (Rounded to 3 significant figures)
Question 18:
ΔKLM is a right-angled triangle
where:
Side KL = Hypotenuse
β = 27°
With respect to 27° angle:
Side KM = Opposite side
∴Trigonometric function used: Sinβ (SOH)
Sin27° = [tex]\frac{Side KM}{0.8 mil}[/tex]
Cross-multiplication is applied:
Side KM = (Sin27°)×(0.8 mil)
Side KM = 0.4 cm (Rounded to 1 decimal places)
Jose pays 10% of his balance each month. If Jose borrowed $5000 with no interest, how much does he still owe after 1 year?
Answer: 1,422
Step-by-step explanation:
Compare and contrast the parabolas with these definitions:
parabola A: points that are the same distance from (0,4) and the x-axis
parabola B: points that are the same distance from (0, -6) and the x-axis
Parabola A and parabola B are similar in that they are both vertically oriented parabolas with the x-axis as their axis of symmetry. However, they differ in their vertex, focus, and directrix, which means they have different equations and open in different directions.
What are the similarity and difference of both parabolaBoth parabola A and parabola B are examples of vertically oriented parabolas that have the x-axis as their axis of symmetry. However, they differ in their vertex, focus, and directrix.
Parabola A has its vertex at (0, 0) and its focus at (0, 4). The directrix is the line y = -4, which is a horizontal line 4 units below the vertex. This means that any point on parabola A is equidistant to the vertex and the focus, and the distance between any point on the parabola and the directrix is equal to the distance between the point and the focus.
Parabola B has its vertex at (0, 0) and its focus at (0, -6). The directrix is the line y = 6, which is a horizontal line 6 units above the vertex. This means that any point on parabola B is equidistant to the vertex and the focus, and the distance between any point on the parabola and the directrix is equal to the distance between the point and the focus.
In terms of their equations, the equation of parabola A is y^2 = 16x, while the equation of parabola B is y^2 = -24x. Notice that parabola B has a negative coefficient of x, which means it opens to the left instead of the right like parabola A.
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solve for x,
3x+10
3x+2
Does a matrix have to be symmetric to be orthogonally diagonalizable?
No, a matrix does not have to be symmetric to be orthogonally diagonalizable. Orthogonal diagonalization is a property of square matrices that can be used to simplify calculations and solve certain types of problems.
A square matrix A is orthogonally diagonalizable if there exists an orthogonal matrix P and a diagonal matrix D such that A = PDP^T, where D contains the eigenvalues of A and P contains the corresponding eigenvectors.
A symmetric matrix is always orthogonally diagonalizable, meaning that there exists an orthogonal matrix P such that A = PDP^T, where D is a diagonal matrix containing the eigenvalues of A. However, not all matrices are symmetric and still can be orthogonally diagonalizable.
For a non-symmetric matrix, the eigenvectors and eigenvalues may not have certain symmetrical properties that make orthogonal diagonalization straightforward, but it is still possible to diagonalize the matrix. In such cases, we can use other techniques, such as the Schur decomposition, to obtain a similar diagonal form.
In summary, a matrix does not have to be symmetric to be orthogonally diagonalizable, but symmetric matrices are always orthogonally diagonalizable. Other techniques may be used for diagonalizing non-symmetric matrices.
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Answer the question for lots of points
The angle of depression from an airplane to the top of an air traffic control tower is 56°. If the tower is 320 feet tall and the the airplane is flying at an altitude of 7,450 feet, how far away is the airplane from the control tower? Round to the nearest tenth.
Find the angle of depression from the top of a lighthouse 275 feet above water to a boat 1,324 feet off shore. Round to the nearest whole number.
Answer:
1) 7995.9 feet
2) 12 degrees
Step-by-step explanation:
1)
We can start by drawing a diagram of the situation. Let's label the height of the tower as "h", the distance from the airplane to the tower as "d", and the angle of depression as 56°.
C (top of tower)
/|
/ |
/ |h
/ |
/θ |
A_____/_____|
d B
In this diagram, point A represents the airplane, point B represents the base of the tower, and point C represents the top of the tower. The angle θ is the angle of depression from the airplane to the top of the tower.
We can use trigonometry to solve for the distance "d" from the airplane to the tower. In particular, we know that:
tan(θ) = h / d
We can rearrange this equation to solve for "d":
d = h / tan(θ)
Substituting the values we know, we get:
d = 320 / tan(56°)
Using a calculator, we can evaluate this to get:
d ≈ 215.8 feet
However, the airplane is flying at an altitude of 7,450 feet, so we need to add this to the height of the tower to get the total distance from the airplane to the ground:
total distance = d + 320 + 7,450
Plugging in the value we found for "d", we get:
total distance ≈ 7995.8 feet
Rounding to the nearest tenth, we get:
total distance ≈ 7995.8 ≈ 7995.9 feet
2)
We can use the tangent function to find the angle of depression. Let theta be the angle of depression. Then:
tan(theta) = (275 / 1324)
We can solve for theta by taking the inverse tangent (or arctan) of both sides:
theta = arctan(275 / 1324)
Using a calculator, we find:
theta ≈ 11.92 degrees
Rounding to the nearest whole number, we get:
The angle of depression is approximately 12 degrees.
Circle � ′ A ′ A, prime is the result of rotating circle � AA by 18 0 ∘ 180 ∘ 180, degrees about point � PP. A coordinate plane. The x- and y-axes both scale by one. A circle with a center at negative three, zero and a radius of two. A point P is plotted at one, negative two. A coordinate plane. The x- and y-axes both scale by one. A circle with a center at negative three, zero and a radius of two. A point P is plotted at one, negative two. Select all of the correct statements about the unchanged properties of circle � AA and circle � ′ A ′ A, prime. Choose all answers that apply: Choose all answers that apply: (Choice A) A Circle � AA and circle � ′ A ′ A, prime have the same circumference. (Choice B) B The radii of circle � AA and circle � ′ A ′ A, prime have the same lengths. (Choice C) C Points � AA and � ′ A ′ A, prime are both on the � xx-axis. (Choice D) D None of the above
Circle A and circle A' have the same circumference and the radii of circle A and circle A' have the same lengths. Therefore, options A and B are the correct answers.
What is rotation?Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.
Given that, circle A' is the result of rotating circle A by 180° about point P.
When we rotate any object its shape and size does not change, only its position changes.
Therefore, options A and B are the correct answers.
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Brianna surveyed a representative sample of students at her school to collect data about the numbers of Internet-compatible devices they own. Use the data in the table. Select all the valid inferences.
Internet-Compatible Devices
Number of Devices Number of Students
1 18
2 25
3 or more 7
Students are more likely to own exactly 2 devices than any other number.
More students own 3 devices than own more than 3 devices.
Less than half as many students own 3 or more devices as compared to students who own 1 device.
10 more students own 1 device than own 3 or more devices.
None of the students own exactly 5 devices.
The statements, Students are more likely to own exactly 2 devices than any other number, Less than half as many students own 3 or more devices as compared to students who own 1 device and About 10 more students own 1 device than own 3 or more devices are true.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Students are more likely to own exactly 2 devices than any other number is
true because the number of students own exactly 2 devices is greater than the other categories.
Less than half as many students own 3 or more devices as compared to students who own 1 device is true because 18 students own 1 device, the half of them is 9, and the number of students own 3 or more devices is 7 which is less than 9.
About 10 more students own 1 device than own 3 or more devices is true because the difference between students own 1 device and those own 3 or more devices = 18 - 7 = 11 which is about 10 more.
Hence, the statements, Students are more likely to own exactly 2 devices than any other number, Less than half as many students own 3 or more devices as compared to students who own 1 device and About 10 more students own 1 device than own 3 or more devices are true.
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Two furniture salesmen are comparing their salaries. Gert is paid R25,00 per hour plus a 15% commission on his total sales. Ben is paid R29,00 per hour plus a 10% commission on his total sales. Suppose each has sold R5 000 worth of furniture, compare their income over various periods of time to find out when they will earn the same. What will happen after that point? Who would have earned more before that point?
When sales are under $15,000, the current job pays less than the new offer. The new job offer is therefore favoured for sales below $15,000.
What is meant by linear equation?A linear equation, according to the definition, is an algebraic equation in which each term has an exponent of one and the graphed value of the equation is a straight line. Y=mx + b is a prime example of a linear equation. Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y). A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables where the value of one (often y) relies on the value of the other (usually x).a) Wc = 2000+.07S
b) Wn =2300+.05S
c) When the totals are similar, the sales level at which she would not care
2000 + .07S = 2300 + .05S
subtract .05S from both sides
2000 +.02S = 2300
subtract 2000 from both sides
.02S = 300
divide both sides by .02
S = 300/.02 = 15000
Sales of $15,000 equate to identical pay.
If we apply the same calculation, substituting less than for the = sign... The result of our equation is
2000 + .07S < 2300 + .05S
S < 15000
The present employment pays less than the new offer when sales are under $15,000. Therefore, the new job offer is preferred for sales below $15,000.
check: Let S = 10,000
Wc = 2000+.07(10000) = $2700
Wn = 2300 + .05(10000) = $2800
As can be seen, at sales of $10,000 the new job earns more.
The complete question is:
A salesperson receives a monthly salary $2000 plus commission of 7% of sales. she is offered a new job at $2300 per month plus commission of 5% os sales.
a) write a linear equation for her current wage W in terms of her monthly sales S.
b)write a linear equation for her monthly wage W of the job offer in terms of her monthly sales S.
c) what level of sales will make her indifferent between the two jobs? Which scheme is preferred when sales are below this level?
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Amy has a job that pays according to the function P(h) = 9.5h. If Amy is only allowed to work
40 hours per week, what are the domain and range of the function P?
Answer:
well in 9.5 40 you have to multiply which is 40 times 9.5h
n the metric system, each millimeter increment is equal to _____.A. 1/1000 of a centimeterB. 1/100 of a centimeterC. 1/10 of a centimeterD. 10 centimeters
The answer is C. 1/10 of a centimeter.
Millie is considering a zero closing cost loan. She wants to borrow $600,000 her lending institution is offering her a 3.49% loan for 25 years. She has the option of purchasing negative points, which will increase her apr by 0.125% for each 1% of her principal credited to her. To cover the bank's closing cost she will need to get 2 negative points. Determine Millie's breakeven time. Is this purchase of negative points a wise decision? Explain.
Breakeven's time is 31.7 years.
The loan term is only 25 years, so it is not a wise decision.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
To determine if the purchase of negative points is a wise decision, we first need to calculate Millie's monthly payment with and without the negative points.
Without negative points:
Principal = $600,000
Interest rate = 3.49%
Loan term = 25 years or 300 months
Now,
Monthly Payment = $2,967.27
With negative points:
Millie needs to purchase 2 negative points to cover the bank's closing cost. Each negative point will increase her APR by 0.125%, so the new interest rate will be:
New interest rate.
= 3.49% + (2 x 0.125%)
= 3.49/100 + (2 x 0.125/100)
= 3.74%
Monthly Payment = $2,998.84
The breakeven time.
This is the amount of time it takes for the cost of the negative points to be offset by the savings in monthly payments.
The total cost of the negative points.
We see that,
Each negative point costs 1% of the principal.
Cost of negative points,
= 2 x $6,000
= $12,000
The breakeven time.
Monthly savings.
= $2,967.27 - $2,998.84
= -$31.57
i.e
The value is negative because the new monthly payment is higher.
So,
Breakeven time.
= $12,000 ÷ -$31.57
= 380.2 months
This is,
1 year = 12 months
so,
31.7 years
Thus,
Breakeven's time is 31.7 years.
The loan term is only 25 years, so it does not make sense to purchase the negative points.
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Given the equation y = -2x + 4, complete the table.
0
1
2
3
Answer:
0: 4
1: 2
2: 0
3: -2
Step-by-step explanation:
To find out the values of 0, 1, 2 and 3 we have to substitute these numbers into the place of x
0...
y = -2(0) + 4 = 4
1...
y = -2(1) + 4 = 2
2...
y = -2(2) + 4 = 0
3...
y = -2(3) + 4 = -2
TIP:
We can see that there is a pattern of decreasing of 2 so to keep finding the following values we just have to keep subtracting 2. For any question like this, if we see a pattern to make it easier and quicker all we have to do is follow the pattern!
Hope this helps, have a lovely day! :)
please help me on this
Answer:
[tex]\frac{4}{90}[/tex]
Step-by-step explanation:
[tex]\frac{4}{9}[/tex] - [tex]\frac{4}{10}[/tex]
to subtract the fractions we require them to have a common denominator
the LCM of 9 and 10 is 90
= = [tex]\frac{4(10)}{9(10)}[/tex] - [tex]\frac{4(9)}{10(9)}[/tex]
= [tex]\frac{40}{90}[/tex] - [tex]\frac{36}{90}[/tex]
= [tex]\frac{40-36}{90}[/tex]
= [tex]\frac{4}{90}[/tex]
If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4. If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Find the fraction.
Answer:
To solve this problem, we need to start by setting up an equation. The equation should express the fact that the result of the two operations on the fractions is both 4 and 5/4.
We can do this by writing:
4x/(x-2) = 4
5x/2(x-2) = 5/4
Solving for x, we get x=16. Therefore, the fraction we are looking for is 4/14, since 4 times 16 divided by 16 minus 2 equals 4 and 5 times 16 divided by 2 times 16 minus 2 equals 5/4.
How Much Tax Will She Pay
The total amount of money Tegan paid for tax last year from her income of £48,300 is £4,830
How Much Tax did Tegan Pay?Tegan's income last year before tax = £48,300
Tegan's earnings is upto £43,000 and in excess of £48,300 - £43,000
= £5,300
Assume, Tegan's tax rate is 10% since her excess is not up to £11,000
Tegan's tax = 10% of £48,300
= 0.10 × 48,300
= £4,830
Ultimately, Tegan paid a total amount of £4,830 as tax last year.
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Change 1.5 to fraction with working
Answer:
³/₂
Step-by-step explanation:
1.5 = ¹⁵/₁₀
= ³/₂
Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 17 centimeters and a height of 13 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
3,203 cm2
2,295 cm2
1,020 cm2
731 cm2
Answer:
2,295 cm2
Step-by-step explanation:
Answer:
(b) 2295 cm²
Step-by-step explanation:
You want the area of icing on a cake 13 cm high and 17 cm in radius.
Icing areaThe area of the top is ...
A = πr²
The area of the side is ...
A = 2πrh
Then the total area of icing on the cake is ...
πr² +2πrh = πr(r +2h)
= 3.14(17 cm)(17 cm + 2·13 cm) = 2295.34 cm²
The area of icing needed for the cake is about 2295 cm².
<95141404393>
In 1997, a city had a population of 250,000 people. Each year since, the population has grown by 4.9%.
Let t be the number of years since 1997. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
Help please…………………………………..
Answer:
35
Step-by-step explanation:
DUDE JUST PLUG IN THE NUMBER.
[tex]x^4 -3x^3 + x -3\\(-2)^4 - 3(-2)^3 + (-2) -3\\16 + 24 -2 - 3\\35[/tex]
El costo de combustible por hora que un tren gasta en su recorrido es de [tex]V^2/5[/tex] pesos donde v es la velocidad en kilómetros por hora Note que el costo depende del cuadrado de la velocidad Otros costos, incluyendo el de mano de obra, son de $400 por hora. Expresa el costo total de un viaje de 500 kilómetros como una función de la velocidad v
The total cost of the trip is a function of the velocity v is:
Cost (v) = 500v + 400/v
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Distance = 500 km
Velocity = v km/h
Now,
Velocity = Distance /Time
Time = distance/velocity
= 500 / v
The total cost of the trip.
Cost = fuel cost per hour x time + other costs per hour x time
= v² x 500/v + 400 x 500/v
= 500 v + 400/v
Thus,
The total cost of the trip is a function of the velocity v is:
Cost (v) = 500v + 400/v
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The complete question.
The cost of fuel per hour that a train spends on its journey is v^2 pesos, where v is the velocity in kilometers per hour. Note that the cost depends on the square of the velocity.
Other costs, including labor, are $400 per hour.
Express the total cost of a 500-kilometer trip as a function of the velocity v.
2.) Emmanuel is at a sporting goods store. The store
offers a 9% discount on all items. At checkout a 6%
sales tax is added to the discounted price. Select the
two that apply.
A. $25 pants cost $24.12 at checkout
B. $89 cleats cost $76.50 at checkout
C. A $29 basketball costs $37.97 at checkout.
D. $189 glove costs $183.33 at checkout
what is 2 + 2 equal and what are the steps to solving it
Answer: 4
Step-by-step explanation:
1+1=2 but if it is 2+2 then it would = 4
PLEASE HELP WITH ALGEBRA!!!
A classmate simplified this rational equation. (Picture attached)
[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}[/tex]
a) circle and explain the error in this simplifcation
b) show your work as you correct the error
Part (a)
The error happens on the 2nd step.
The student multiplied both sides by the LCD (x+3)(x-3) to clear out the fractions, but forgot about the first "1" at the very left.
=================================================
Part (b)
[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\(x+3)(x-3)*1 - (x+3)(x-3)*\frac{2}{x+3} = (x+3)(x-3)*\frac{x+1}{x-3}\\\\(x+3)(x-3) - 2(x-3) = (x+1)(x+3)\\\\x^2-9 - 2x+6 = x^2+4x+3\\\\x^2-2x-3 = x^2+4x+3\\\\x^2-2x-3-x^2-4x-3=0\\\\-6x-6=0\\\\-6x=6\\\\x = 6/(-6)\\\\x = -1[/tex]
The answer is x = -1Check:
[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\1 - \frac{2}{-1+3} = \frac{-1+1}{-1-3}\\\\1 - \frac{2}{2} = \frac{0}{-4}\\\\1 - 1 = 0\\\\0 = 0\\\\[/tex]
The answer is fully confirmed.
You can use a graphing tool like GeoGebra to visually confirm the answer.
I will give you a Brainliest
Answer:
192
Step-by-step explanation:
2x9=18
18x12=192
Given f(x) = 2x - 1, find the value of f(-1).
To find the value of f(-1), we simply need to substitute -1 for x in the function f(x) = 2x - 1 and evaluate:
f(-1) = 2(-1) - 1
= -2 - 1
= -3
Therefore, the value of f(-1) is -3.
Answer:
f=2x-1/x
Step-by-step explanation:
I hope this helps :) <3
Find the measure of angle B
Equation form
The measure of the angle B in the triangle is 51.34 degrees.
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The triangle above is a right angle triangle. A triangle is right triangle because one of its angles is 90 degrees.
The angle of a right triangle can be found using trigonometric ratios as follows:
tan B = opposite / adjacent
tan B = 25 / 20
B = tan⁻¹ 5 / 4
B = tan⁻¹ 1.25
B = 51.3401917459
Therefore,
B = 51.34 degrees
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