The minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm are 3 cm and 39 cm, respectively.
What is triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points. The three sides and three angles of a triangle are interconnected by various geometrical principles and formulas, such as the Pythagorean theorem, trigonometric ratios, and the Law of Cosines. Triangles are commonly classified based on their side lengths and angles, including equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are also used in various real-life applications, such as in architecture, engineering, and physics.
According to given information :To complete a triangle with side lengths 18 cm and 21 cm, the length of the third side must be such that it satisfies the triangle inequality. The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.
Let x be the length of the third side. Then we have:
18 + 21 > x
18 + x > 21
21 + x > 18
Simplifying each inequality, we get:
x < 39
x > 3
x > -3 (since length cannot be negative)
The minimum value of x is 3 cm (when the two sides form a degenerate triangle), and the maximum value of x is 39 cm (when the three sides form an equilateral triangle). Therefore, the minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm are 3 cm and 39 cm, respectively.
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What is the result of multiplying the first equation by 2 and adding to the second equation?
6x − y = 7
2x + y = 5
A. 14x + 3y = 19
B.14x + y = 19
C.14x - y = 19
find x, please show the work
The table below represents a linear function for the cost of a gym membership based on the number of months of membership.
What is the slope and y-intercept of the linear function.
The equation of line is y = 30x + 75 , where the slope is m = 30 and the y intercept is 75
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 1 , 105 )
Let the second point be Q ( 3 , 165 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 165 - 105 ) / ( 3 - 1 )
Slope m = ( 60 / 2 )
Slope m = 30
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 105 = 30 ( x - 1 )
On simplifying the equation , we get
y - 105 = 30x - 30
Adding 105 on both sides of the equation , we get
y = 30x + 75
Hence , the equation of line is y = 30x + 75
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If you take - 3/10 of a number and add 1, you get 10. Write an equation to represent the situation. What is the original number
Answer: -30
Let's call the original number "x". Then, we can write the equation as follows:
-3/10 x + 1 = 10
To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:
-3/10 x = 9
x = (9 * 10)/(-3)
x = -30
So, the original number is -30.
Choose the best answer.
A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a
A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a conditional statement.
What is the conditional statement?A conditional statement is one that has the form "If P then Q," where P and Q are sentences. P is referred to as the hypothesis in this conditional statement, and Q is referred to as the conclusion. "If P then Q" implies that Q must be true sometimes when P is true.
The type of conditional statements are as follows:
General truth: I feel better all day if I eat breakfast.Future event - I will investigate tonight if I have a scan tomorrow.Assumption: If I had a million dollars, I would purchase an airplane!Hypothetical outcome - I might have been offered the position if I had geared up for the interview.A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a conditional statement.
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Suppose that n 0 and n 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P (x) y = Q(x) y^n into the linear equation dy/dx +(1-n)p(x)v(x)=(1-n)q(x).
The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:
The equation is in the form
dy/dx +P(x)y=Q(x)yⁿ, where P and Q are functions of x or constants, this is called Bernoulli's equation.
Now, we have to substitution using
[tex]v = {y}^{1 - n} [/tex]
Differentiating both side with respect to 'x'
[tex]v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'[/tex]
we get,
[tex]= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)[/tex]
Now, by using
[tex]v' = {y}^{1 - n} [/tex]
The given equation is expressed as:
[tex]v + (1 - n)p(x)v = (1 - n)q(x)[/tex]
or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)
The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.
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Points A, B, C and D are collinear, with B between A and C, and C between B and D. What is the measure of CD, if AB = 4x-1, BC= 6x-2, BD = 11x + 5, and AD = 64?
A. 15 units
B. 22 units
C. 25 units
D. 27 units
E. 33 units
Answer:
D. 27 units.
Step-by-step explanation:
See my attachments.
How do you write Euler's number in Symbolab?
To write Euler's number in Symbolab, you can simply use the notation "e". For example, if you want to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.
Euler's number, denoted as "e", is a mathematical constant that is approximately equal to 2.71828. To write Euler's number in Symbolab, you can simply use the letter "e" in lowercase. For example, to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.
Alternatively, if you want to use the built-in function for Euler's number in Symbolab, you can use the "exp(x)" notation, where x is the exponent. For example, to evaluate e raised to the power of 2, you can enter "exp(2)" in Symbolab. Symbolab supports various mathematical functions and constants, including trigonometric functions, logarithmic functions, and mathematical constants, which can be used to solve various mathematical problems.
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What is the average increase in pennies for Daisy's piggy bank over the first 2 days (starting with day 0)?
The average increase in first 2 days is 1.5 pennies/day.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Given is a tabular data about Daisy's piggy bank.
The average increase in first 2 days -
{a} = (7 - 4)/(2 - 0)
{a} = 3/2
{a} = 1.5
Therefore, the average increase in first 2 days is 1.5 pennies/day.
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Select all of the expressions that have a positive value based on the positions of a and b.
(Select all that apply.)
1. -b
2. a+b
3.a-b
4. a*b
5. -b/a
The expressions that have a positive value based on the positions of a and b are a + b and a×b. options 2 and 4
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of terms, variables, factors and constants.
These expressions are also composed of mathematical operations such as;
SubtractionBracketParenthesesMultiplicationAdditionDivisionFloor divisionGiven the expressions;
a+ b and a×b.
They have the variables both positive
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Find the number of sides (n) of the polygons with the angle values shown in the items below.
a) The sum of the interior angles is 10,440∘
b) The value of each interior angle is 171∘
As per the concept of polygon,
a) The sum of the interior angles is 10,440° then the number of sides is 58
b) The value of each interior angle is 171°, then the number of sides is 36
A polygon is a two-dimensional geometric shape made up of straight lines and angles. The number of sides a polygon has is directly related to the sum of its interior angles.
a), we can use the formula for the sum of the interior angles of a polygon, which is (n-2) times 180 degrees, where n is the number of sides. To find n, we can rearrange the formula to
=> n = (sum of interior angles / 180) + 2.
Plugging in the value of 10,440 degrees for the sum of interior angles, we get
=> n = (10440 / 180) + 2 = 58.
Therefore, the polygon in item a) has 58 sides.
For item b), we can use the formula for the value of each interior angle of a regular polygon, we get
=> n = (180(n-2)) / 171 = (180n - 360) / 171.
Solving for n, we find that the polygon in item b) has 36 sides.
In conclusion, polygons with the angle values shown in items a) and b) have 58 and 36 sides respectively. These formulas can be applied to any polygon to find the number of sides based on its interior angle values.
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8 A crystal paperweight
is shaped like a cylinder with a star-shaped hole. The
top of the star-shaped hole is shaped like a square with four points that are
identical equilateral triangles. The height of the cylinder is 3 centimeters. Find
the volume of the paperweight.
Please Help ASAP!!!
The volume of the paperweight is 79.3 cm³.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
From the given information, The area of the star-shaped cutout is,
A square has a side length of 2 cm, and four equilateral triangles have a side and a height of 2 cm.
So, The area of the star-shaped cutout is,
= (2×2) + 4×(1/2)×2×2.
= 4 + 8.
= 12 cm.
Now, The volume of the star-shaped cut-out is,
= 12×height,
= 12×3.
= 36 cm³.
And the volume of the cylinder is,
= π(1 + 2 + 0.5)²×3.
= π(3.5)²×3.
= 115.4 cm³
Therefore, The volume of the paperweight is,
= 115.4 - 36 cm³.
= 79.3 cm³.
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How many nets are there for a triangular pyramid?
The net of a triangular pyramid consist of a total of 4 triangles. it has 4 faces with the base being one of them which is also in the shape of a triangle.
A net of the triangular pyramid is the pattern formed when the surface of it is laid out flat showing each triangular face of the figure, therefore we know that the net of a triangular pyramid consist of a total of 4 triangles.
Triangular pyramid is a pyramid which has a triangular base. In geometry, vertices are essentially corners. All triangular-based pyramids, either regular or irregular, have four vertices.
It has 6 edges, 4 faces, 4 vertices.
A regular triangular pyramid has equilateral triangles all four faces
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Which statements are correct about the average rate of change for the function
given in the table?
x y
1 1
2 3
3 7
4 15
Select all correct answers.
Select 2 correct answer(s)
The correct answer is the rate of change is 6 over interval 1 ≤ x ≤ 4 and the rate of change is 6 over interval 2 ≤ x ≤ 4
What is the rate of change?Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. In general, the formula for rate of change is: R = (D2 - D1)/T. where: R = rate of change.
Given that is a table, we need to find the average rate of change for the function,
a = 1, f(a) = 1
b = 2, f(b) = 3
Average rate of change is given by = f(b)-f(a) / b-a
= 3-1 / 2-1
= 2
a = 3, f(a) = 7
b = 4, f(b) = 15
Average rate of change is given by = f(b)-f(a) / b-a
= 15-7 / 4-3
= 8
a = 2, f(a) = 3,
b = 3, f(b) = 7
Average rate of change is given by = f(b)-f(a) / b-a = 4
Hence, the correct answer is the rate of change is 6 over interval 1 ≤ x ≤ 4 and the rate of change is 6 over interval 2 ≤ x ≤ 4
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Select all the equations that are equivalent.
52 = 8n + 4
4(2n + 1) = 52
4 = 52 – 8n
4n = 48
n = 6
The equivalent equations are 52 = 8n + 4, 4(2n + 1) = 52 and 4 = 52 – 8n.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To determine which equations are equivalent to each other, we can simplify and manipulate each equation to see if they have the same solution(s).
52 = 8n + 4 can be simplified by subtracting 4 from both sides:
48 = 8n
n=6
Now 4(2n + 1) = 52
8n+4=52
8n=48
n=6
So the 52 = 8n + 4 and 4(2n + 1) = 52 are equivalent equations.
Now 4 = 52 – 8n
8n=52-4 is also equivalent equation.
4n=48 and n=6 are also equal but they are not in the same form as above equations.
Hence, 52 = 8n + 4, 4(2n + 1) = 52 and 4 = 52 – 8n are equivalent equations.
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can someone explain the questions attached? thanks
The probability of landing on the head side of coin and rolling a 3 on the die is found as 1/12.
Explain about the term sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of feasible experiment results. Depending on the experiment, a sample area could contain a variety of results.Sample space for tossing a coin: (H,T)
P(head) = 1/2
Sample space for tossing a dice : (1, 2, 3, 4, 5, 6)
P(3) = 1/6
So,
Probability of head with 3 on the die = 1/ 2* 1/6 = 1/ 12
Thus, the probability of landing on the head side of the coin and rolling a 3 on the die is found as 1/12.
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The correct question is-
A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.
Enter your answer as a fraction in the form a/b (for example 2/3, 5/7) or as an integer.
Solve for x . circles tangent 1 A. 12 B. 10 C. 42 D. 9
8 is the measure if the angle x in the given diagram.
Circle geometryThe point where two lines meet is known as an angle. The given diagram is a circle geometry.
Using the theorem, angle at the arc is twice the angle at the vertex, we will have:
80 = 2(4x + 8)
80/2 = 8x + 8
40 = 4x + 8
4x = 40 - 8
4x = 32
x = 32/4
x = 8
Hence the value of x from the diagram given is 8
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f(x)=x² +16x-24 and
g(x)=x²-5x-17, find (ƒ + g)(x).
If functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given functions are f(x)=x² +16x-24 and g(x)=x²-5x-17.
We need to find (ƒ + g)(x).
From properties we have (ƒ + g)(x)=f(x)+g(x)
(ƒ + g)(x)=x² +16x-24+x²-5x-17.
Add the like terms
(f+g)(x)=2x² +11x-41
Hence, if functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.
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Which number is a factor of 24 but not a multiple of 12
1. Arturo earns n dollars per hour. Next month
he will receive a 2% raise in pay per hour. The
expression n +0.02n is one way to represent
Arturo's pay per hour after the raise. Write
an equivalent simplified expression that will
represent his pay per hour after the raise.
The equivalent simplified expression is 1.02n.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Given that, Arturo earns n dollars per hour. Next month he will receive a 2% raise in pay per hour.
The expression n +0.02n is one way to represent Arturo's pay per hour after the raise.
Here, the equivalent expression is n +0.02n= 1.02n
Therefore, the equivalent simplified expression is 1.02n.
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Paul, Maria, Stephanie, and Andy have a total of $56 to spend at the amusement park. Admission will cost them $5 each for a total of $20. They can spend the rest on food and rides. They plan to spend twice as much on rides as on food. How much do they plan to spend on rides?
Answer:
They plan to spend $24 on rides.
Step-by-step explanation:
Let the amount they spend on food be x.
ride : 2x
amount left= $56-$20
= $36
2x+x= 36
x=12
2x= 2(12)
= 24
A cylinder-shaped scoop has a base radius of 2 centimeters and a height of 5 centimeters. The scoop has a mass of 14.9 grams when empty. The scoop is completely filled with water. One cubic centimeter of water has a mass of one gram. What is the mass of the scoop of water in grams, including the mass of the scoop? Describe how you found your answer. Round to the nearest tenth.
Answer:
77.7 g
Step-by-step explanation:
You want the mass of a cylindrical scoop of radius 2 cm and height 5 cm when it is filled with water at 1 g/cm³, and has an empty mass of 14.9 g.
WaterThe mass of the water will be the product of its volume and its density. The volume is that of a cylinder with radius 2 cm and height 5 cm. That volume is given by the formula ...
V = πr²h = π(2 cm)²(5 cm) ≈ 62.83 cm³
The mass of the water is then ...
(62.83 cm³) × (1 g/cm³) = 62.83 g
Total massThe total mass of the water-filled scoop is the sum of its empty mass and the mass of the water:
scoop + water = 14.9 g + 62.8 g = 77.7 g
The mass of the scoop and water is 77.7 grams.
x^2+y^2=100 is it a function?
The equation x^2+y^2=100 is not a function
How to determine if it is a functionFrom the question, we have the following parameters that can be used in our computation:
x^2 + y^2 = 100
The above equation is a circle equation
As a general rule, we have
Circle equations are not functions and they do not represent a function on a graph
Hence, x^2+y^2=100 is not a function
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Mateo currently has $100 in his bank account and plans on saving $20 per week in order to save for soccer camp over the summer. Write an equation to represent the amount of money saved, S, with respect to the number of weeks that have passed, w.
S = _ w + _
The equation that represents the amount of money saved is S = $100 + $20w
What is the equation that represents the amount of money saved?The equation that represents the amount of money saved is a linear equation . A linear equation is an equation that has a single variable raised to the power of 1.
The form of the linear equation is:
Total money saved = amount in the bank + (amount that would be saved each week x number of weeks)
S = $100 + ($20 x w)
S = $100 + $20w
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If f is differentiable at a, must f be continuous at a? A. No, if f is differentiable at a and does not have a corner at a, then f is continuous at a B. No, if f is differentiable at a and does not have a vertical tangent at a, then f is continuous at а. C. No, if f is differentiable at a and positive at a, then f is continuous at a. D. Yes, iff is differentiable at a, then fis continuous at a.
The correct statement regarding the continuity of differentiable functions is given as follows:
D. Yes, if f is differentiable at a, then f is continuous at a.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
For a function to be classified as differentiable, the function must be continuous, plus the first derivative of the function must also be continuous.
This means that all differentiable functions are continuous, and thus the correct option is given by option D.
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a || b and p is a transversal. If m 1 = 140°, find the
measure of each angle giving one reason for each answer.
(The first one is done for you.)
Answer:
Angle 4 = 140
Angle 3= 40
Angle 5=140
angle 6=40
angle 7=40
Step-by-step explanation:
Adjacent angles are congruent. Thats how I can tell angle 4 is 140. And also how i can tell angle 3 is 40. Any questions?
im not explaining the rest im too tired
btw I also do 8th math lol it stinks.
What is the connection string for SQL Server using Windows Authentication?
The connection string for SQL Server using Windows Authentication is as follows:
Server=myServerAddress;Database=myDataBase;Trusted_Connection=True;
Specify the server address in the format "Server=myServerAddress". Replace "myServerAddress" with the name or IP address of the SQL Server instance you want to connect to.
Specify the name of the database you want to connect to in the format "Database=myDataBase". Replace "myDataBase" with the name of the database.
Use Windows Authentication by setting "Trusted_Connection=True". This means that the user running the application is authenticated using their Windows credentials, rather than a SQL Server login.
Use semicolons (;) to separate the different parts of the connection string.
Using Windows Authentication is a more secure and convenient way to connect to a SQL Server database, as it eliminates the need to store and manage login credentials in the application.
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Two important ingredients for baking bread are
yeast and flour. To make a loaf of bread of at
most
30 servings, maintain a yeast to
flour ratio of 1:200. If you're making a loaf of more than 30
servings, use a ratio of 1:180.
If you're making 30 servings
of bread and using 0.25 oz of yeast, how many ounces of flour do you
need?
If you're making 60 servings of bread and using 540 oz of flour, how many ounces of yeast do you
need?
NOTE: Enter only numerals for each of your answers.
If you're making 60 servings of bread and using 540 oz of flour, then the number of ounces of yeast you need is 3 oz.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, to make a loaf of bread of at most 30 servings, maintain a yeast to flour ratio of 1:200. If you're making a loaf of more than 30 servings, use a ratio of 1:180.
If you're making 30 servings of bread and using 0.25 oz of yeast, then
0.25/Flour = 1/200
Flour = 50 oz
If you're making 60 servings of bread and using 540 oz of flour, then
Yeast/540 = 1/180
Yeast = 3 oz
Therefore, if you're making 30 servings of bread and using 0.25 oz of yeast, then the number of ounces of flour you need is 50 oz.
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the sum of 3 consecutive multiples of 8 is 888 find the multiples
[tex]\fbox{\textbf{288, 296, and 304}}
[/tex]
Step-by-step explanation:Let's assume the first multiple of 8 is x, then the second multiple is x+8, and the third multiple is x+16.According to the problem statement, the sum of these three multiples is 888:x + (x+8) + (x+16) = 888Simplifying the left side:3x + 24 = 888Subtracting 24 from both sides:3x = 864Dividing both sides by 3:x = 288Therefore, the first multiple of 8 is 288, the second is x+8 = 296, and the third is x+16 = 304.So, the three consecutive multiples of 8 that add up to 888 are 288, 296, and 304Find the value of each variable
The triangle on the left is a 45 45 90 triangle and the triangle on the right is a 30 60 90 triangle.
In a 45 45 90 triangle, the length of the hypotenuse is equal to the length of either one of the legs times the square root of 2. So that means that a and c are both 18.
In a 30 60 90 triangle, the length of the hypotenuse is twice that of the leg opposite the 30 degree angle. So that means that b is 36. The length of the leg opposite the 60 degree angle is the length of the other leg times the sq root of 3. So that would give you d = 18 sq root 3.