(will give brainliest!!!)
In the right △ABC with m∠C=90°, m∠B=75°, and AB = 12 cm. Find the area of △ABC.
(no sin and cos pleasee)
(show work too)
Answers
9514 1404 393
Answer:
18 cm^2
Step-by-step explanation:
Under the given constraints, the way to find the area of this triangle is to use a triangle solver app or web site. The attached shows the area is 18 cm^2.
_____
A simple way to find the area is to use the cosine function to find side AC adjacent to the 75° angle. Then use the formula for area that uses the sine function.
AC = AB·cos(75°)
Area = (1/2)AB·AC·sin(75°)
Area = (1/2)(AB²)cos(75)sin(75°)
= (1/4)AB²·sin(150°) . . . using the double-angle identity
= (1/4)(12 cm)²(1/2)
Area = 18 cm²
__
The useful relations are ...
Cos = Adjacent/Hypotenuse
cos(75°) = AC/AB ⇒ AC = AB·cos(75°)
and ...
Area = (1/2)pq·sin(α) . . . . for two sides p and q with angle α between them
Area = (1/2)AB·AC·sin(75°)
Another identity we used here is ...
sin(2α) = 2sin(α)cos(α) ⇔ sin(α)cos(α) = (1/2)sin(2α)
Putting these together, the formula for area we used was effectively ...
A = (1/4)AB²sin(2·75°)
Related Questions
the relationship between altitude and the boiling point is linear.AT an altitude of 8300ft 8300 ft , the liquid boils at 194.23 194.23 degrees Fahrenheit an altitude of 4200 ft , 4200 ft , the liqiud boils at 202.02 202.02 degrees fahrenheit.Write an equation giving the boiling point b b of the liquid,in degrees fahrenheit in terms of altitude a in feet . feet . What is the boiling point of the liqud at 2600 ft 2600 ft
Answers
Complete Question
The relationship between altitude and the boiling point is linear. At an altitude of 8300ft, the liquid boils at 194.23 ° F
At an altitude of 4200 ft , the liquid boils at 202.02° F.
Write an equation giving the boiling point b of the liquid, in terms of altitude a in feet . feet . What is the boiling point of the liquid at 2600ft
Answer:
The equation is [tex]y = -0.001943x + 210.3569 [/tex]
At 2600ft the temperature is [tex]y = 205.3051 \ °F [/tex]
Step-by-step explanation:
From the question we are told that
The temperature at 8300ft is 194.23 ° F
The temperature at 4200 ft is 202.02° F
Generally the slope for this relationship is mathematically represented as
[tex]m = \frac{ 202.2 - 194.23}{ 4200 - 8300}[/tex]
=> [tex]m = 0.001943 ^o F / ft [/tex]
Generally the according to the point slope formula is
[tex]y - y_1 = m(x -x_1 )[/tex]
=> [tex]y - 194.23 = -0.001943 (x - 8300 )[/tex]
=> [tex]y - 194.23 = -0.001943x + 16.1269 [/tex]
=> [tex]y = -0.001943x + 210.3569 [/tex]
Now we are given from the question that x = 2600 ft
Then
[tex]y = -0.001943(2600) + 210.3569 [/tex]
=> [tex]y = 205.3051 \ °F [/tex]
Which expression isequivalent to (65) (62)?
Answers
sid has £5 to buy apples and bananas
Answers
Answer:
So he could use 3 pounds for apples, and two for bananas.
Step-by-step explanation:
Jordan doesn't know how to graph y > 2x + 1 . Can you explain to him using the words below how to do it?
Vocabulary to use:
slope, y-intercept, shade above/below, and dotted/solid line
Answers
Answer:
Step-by-step explanation:
Formula: Y= mx+b
m = slope | b = y-intercept
Equation: Y>2x+1
The Y-Intercept is the (1)
Shade above the dotted line because it is >.
You always shade on the left if the left side of the equation is > than the right.
If ≥ Then the line is Solid |||| If > Then the line is dotted.
On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is LaTeX: t=\frac{1}{500}dt=1500d. How long will it take the airplane to travel 800 miles?
Answers
Answer:
1.6hours
Step-by-step explanation:
We know that Speed= distance/ time
But from the question, An equation relating the distance traveled in miles d to the number of hours flying t is t= 1/500d.
And the distance is given as 800 miles
Then, what we need is to substitute the given Distance into the equation of time.
t= 1/500d. Where d= 800 miles
t= (1/500) × 800 miles
t= 800 miles/500
t= 1.6hours
Hence, it will take the airplane to travel 800 miles , 1.6hours
are some integers irrational
Answers
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)?
Answers
Answer:
C) y − 5 = −(x − 2)
Step-by-step explanation:
Solve for b : 1/2b+G=D
Answers
Answer:
I believe the answer is b=1/2(d-g)
Step-by-step explanation:
multiply to remove the variable from the denominator.
The midpoint of TP is (3,0). If one endpoint, point T, has the coordinates
(-2,-6), what are the coordinates of the other endpoint of TP?
Answers
Answer: (7, 6)
Step-by-step explanation: Use the midpoint formula but instead you’re finding the coordinates of the other point(not sure if that makes sense). There’s a shorter way tho
Find the value of x.
Answers
Answer: 12.65
Step-by-step explanation:
Ive never solved a problem like this, but this is how I would solve it. You first want to find the height of the triangle by using the Pythagorean theorem. Solve for the height by using the left triangle.
[tex](4\sqrt{2} )^2=4^2+b^2\\32=16+b^2\\16=b^2\\b=4[/tex]
b is the height, the dotted line, of both triangles. Now do the Pythagorean theorem on the right triangle to find the value of x
[tex]12^2+4^2=x^2\\144+16=x^2\\160=x^2\\x=\sqrt{160} \\x=12.649=12.65[/tex]
A dozen of roses cost $64.44. How much did each rose cost?
Answers
Answer:
5.37
Step-by-step explanation:
if 12 roses cost 64.44 and the price of one is x then
12x=64.44
x=64.44/12
x=5.37
Solve for x
X-5=-9
(10 points)
Answers
x-5 = -9
add 5 to both sides
x = -4
Answer:
x = - 4
Step-by-step explanation:
x - 5 = -9
=> x = -9 + 5
=> x = - 4
Plz help quick >_< What is the best estimate for 81.9 x 4.6?
O A) 100
OB) 360
OC) 400
OD 8,000
Answers
Answer:
B.
Step-by-step explanation:
When you multiply the two decimals you get 376.74 which is closer to 360 than 400
it's b
Step-by-step explanation:
I took the test
PLS HELP PLSSSSSSS QUICK
Answers
(13.2 + 11.9 + 11.8 + 9.7 + x)/5 = 12.2
46.6 + x/5 = 12.2
46.6 + x = 61
x = 14.4
the heaviest fish weighs 14.4 lbs
I WILL GIVE CROWN WHO ANSWERS CORRECTLY
Answers
you need to change the equation to y=mx+b
we have 6x-4y=2 what we need to do is take the 6x and put it on the other side so it’ll be: -4y=-6x+2 we then divide everything by -4 and the answer should be: y=1.5x-0.5.
you then change the second equation. Which is -2y+3x=1 we are going to follow the steps as the first equation we did so you divide everything by -2 because we want the y to be 1. It should look like this y=1.5x-0.5.
As you can see they are the same equation so that means they are in the same line so by that they’re be infinitely many solutions.
Hope this helps.
If mZ3 = 74°, find each measure.
Answers
Answer:
m<1 = 74
m<2 = 74
m<4 = 74
Step-by-step explanation:
The Campbells went out to dinner at Chilli's. They spend $64.00 and want to leave a 20% tip. How much did they tip their server?
Answers
Answer:
12.8$
Step-by-step explanation:
20% is equal to 0.2. You multiply 64 by 0.2. I hope this helps.
The Esteban family will order one T-shirt for each person who attends their family reunion. The cost is $6.50 per T-shirt plus a one-time printing fee of $35.00. This can be represented by the equation c= 6.5n+35, where c represents the total cost of the shirts and n represents the number of shirts ordered. If the family can spend no more than $2,000.00 on T-shirts, what is the maximum number they can order?
Answers
Answer: 302
Step-by-step explanation:
Which of the following is not true?
Answers
Answer:
d) 1/2 ÷ 4 = 1/2 • 4/1
Step-by-step explanation:
when dividing fractions use keep change flip (keep the first fraction, change the sign to multiplication, flip the second fraction)
when multiplying just multiply straight across
Charlene Langhorst's gross weekly salary is $680. Her federal withholding is $101.62. Her employer takes out the standard rates for FICA (Social Security/Medicare). The state tax is 1.5% of gross pay. Each week she pays $32.40 for medical insurance. What are Charlene's total weekly deductions? *
Answers
Answer:
Total deductions = $196.24
Step-by-step explanation:
Gross weekly salary = $680
federal holding = $101.62
FICA standard rate = 7.65% of gross earnings
= 7.65% of $680 = 0.0765 × 680 = $52.02
∴ FICA deductions = $52.02
state tax = 1.5% of gross pay = 1.5% of $680
state tax = 0.015 × 680 = $10.2
∴ state tax = $10.2
Medical insurance = $32.40
Total Deductions = 101.62 + 52.02 + 10.2 + 32.40 = $196.24
-4 5/6 + (3 1/3) =
How dI you do this?
Answers
I REALLY REALLY NEED HELP
Answers
Answer:
answer all?
Step-by-step explanation:
Answer:
1- SF: 2; X:7
2- SF:2.5; X:10.5
3- SF:1.5; X:7.5
4- SF:3; X:9.4
Step-by-step explanation:
Triangle ABC is dilated by a scale factor of 4. If A is located at (3,-5), where will A’ Be located?
Answers
Answer:
Step-by-step explanation:
Multiply both numbers by 4. That is your new coordinates. (12,-20)
Write a biconditional statement for: A prime number has only 1 and itself as factors. What is the truth value?
Answers
Answer:
The statement is;
A number is a prime number if and only if it has 1 and itself as factors
The truth value of this statement is true T
Step-by-step explanation:
The biconditional statement will use the statements if and only if.
Thus, we have;
A number is a prime number if and only if it has only 1 and itself as factors
The truth value of the biconditional statement is T ( true)
What’s the answer xx
Answers
Step-by-step explanation:
Hey there!
Given;
ABC is a Right angled triangle.
Taking angle "A" as reference angle, we get;
Perpendicular (p) = BC
hypotenuse (h) = 13cm
Base(b) = 8cm
We know;
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex]or; \: p(BC) = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
[tex] BC = \sqrt{ {13}^{2} - {8}^{2} } [/tex]
[tex] BC = \sqrt{169 - 64} [/tex]
[tex] BC = \sqrt{105} [/tex]
[tex] BC = 10.246[/tex]
Therefore, BC = 10.246cm.
Hope it helps...
what makes -1.3 a non integer
Answers
Answer:
Decimal and fractions numbers are non-integers
Step-by-step explanation:
The answer is the third choice because integers are whole numbers that can be positive, negative, or zero. -1.3, however, is not a whole number, so it is not an integer. The reason is the third choice as decimals and fractions are not integers. Hope it helps!
√27
A. 3√3
B. 6√7
Which one?
Answers
Answer:
√27 = A. 3√3
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form:
3 √ 3
Ethan builds two different kinds of chairs, rockers and swivels. It takes him 3 hours to build a rocker and requires 2 oz of stain. It takes him 2 hours to build a swivel chair and requires 8 oz of stain. Ethan has 56 oz of stain available and he can only work up to 24 hours. He makes $12 profit on each rocker and $10 profit on each swivel chair. 1. Since there cannot be negative chairs, create two constraints to represent this. 2.Create a constraint for the hours it takes to build the chairs. 3. Create a constraint for the stain it takes for the chairs. PLEASE HELP
Answers
Answer:
(1) [tex]x\geq 0\; \text {and}\;y\geq 0[/tex]
(2) [tex]3x + 2y\leq[/tex] 24
(3) [tex]x+4y\leq 28[/tex]
Step-by-step explanation:
Let x and y be the numbers of rockers and swivels made by Ethan.
(1) Since the number of chairs can't be negative. So,
x\geq0 and y\geq 0 are the two constraints.
(2) He can work a maximum of 24 hours.
The time required to make 1 rocker chair and 1 swivels chair are 3 hr and 2 hr respectively.
So, the time required to make x rocker chair = 3x hr
and the time required to make y swivel chair = 2y hr.
The total time required is 3x + 2y hr which can't be more than the available time, 24 hr.
So, the required constraint is
[tex]3x + 2y\leq 24[/tex]
(3) Similarly,
As 1 rocker chair requires 2 oz strain and 1 swivel chair required 8 ox strain.
So, to make x rocker chair 2x oz required and make y swivel chair 8y oz required which can't be more than the available oz, 56.
So, the required constraint is
[tex]2x + 8y\leq 56[/tex]
[tex]\Rightarrow x+4y\leq 28.[/tex]
Zach's car travels 21 miles on 1 gallon of gas. Using the answer choice from the previous question, Determine how far Zach travels on a trip if he uses 16 gallons of gas.
Answers
Answer:
336 miles
Step-by-step explanation:every gallon goes 21 miles so
2gallons= 42 miles
3gallons =63 miles
16 gallons x 21 miles
Answer:
336
Step-by-step explanation:
for every one gallon he goes 21 miles
21+21=42 2 gallons
42+42=84 4 gallons
84+84=168 8 gallons
168+168=336 16 gallons
label the slope and y intercept
Answers
Slope is 3/2