Movie Theater Screen
Theater Screen: 76 ft. Height: 30 ft.; Width:Use the spaces provided below to calculate the missing measurement for each of the 6
types of screens. You are looking for the width, height, OR the diagonal. You must show
all steps in your work. The size of a screen is given by the length of its diagonal.
Round your answer to the nearest whole inch.
To calculate the missing measurement for each type of screen, we will use the Pythagorean theorem, which states that in a right triangle, the square of the diagonal is equal to the sum of the squares of the other two sides.
1. Finding the diagonal:
We are given the height (30 ft) and width (unknown) of the theater screen. Let's say the width is W.
Using the Pythagorean theorem, we can write the equation as:
D^2 = H^2 + W^2
D^2 = 76^2 + W^2
2. Finding the height:
We are given the width (unknown) and the diagonal of the screen. Let's say the width is W, and the diagonal is D.
Using the Pythagorean theorem, we can write the equation as:
D^2 = H^2 + W^2
H^2 = D^2 - W^2
H = sqrt(D^2 - W^2)
3. Finding the width:
We are given the height (unknown) and the diagonal of the screen. Let's say the height is H, and the diagonal is D.
Using the Pythagorean theorem, we can write the equation as:
D^2 = H^2 + W^2
W^2 = D^2 - H^2
W = sqrt(D^2 - H^2)
Now, we can calculate the missing measurement for each type of screen:
Rectangle Screen:
Given: Height = 30 ft, Width = W (unknown), and Diagonal = 76 ft.
Using the Pythagorean theorem equation:
76^2 = 30^2 + W^2
W^2 = 76^2 - 30^2
W = sqrt(76^2 - 30^2)
Square Screen:
Given: Diagonal = 76 ft.
In a square, all sides are equal, so the height (H) and width (W) are the same.
Using the Pythagorean theorem equation:
76^2 = H^2 + H^2
2H^2 = 76^2
H^2 = 76^2 / 2
H = sqrt(76^2 / 2)
W = H
Triangle Screen:
Given: Height = 30 ft, Width = W (unknown), and Diagonal = 76 ft.
Using the Pythagorean theorem equation:
76^2 = 30^2 + W^2
W^2 = 76^2 - 30^2
W = sqrt(76^2 - 30^2)
Circle Screen:
Given: Diagonal = 76 ft.
In a circle, the diameter is equal to the diagonal. So the diameter (D) is 76 ft, and we can calculate the radius (r) as D/2.
r = D/2 = 76/2
Ellipse Screen:
Given: Height = 30 ft, Width = W (unknown), and Diagonal = 76 ft.
Using the Pythagorean theorem equation:
76^2 = 30^2 + W^2
W^2 = 76^2 - 30^2
W = sqrt(76^2 - 30^2)
can you make it shorter
Certainly! Here is a shorter version:
1. Rectangle Screen:
Given: Height = 30 ft, Width = W (unknown), Diagonal = 76 ft.
Using the Pythagorean theorem: W = sqrt(76^2 - 30^2)
2. Square Screen:
Given: Diagonal = 76 ft.
Height (H) and width (W) are the same. H = W = sqrt(76^2 / 2)
3. Triangle Screen:
Given: Height = 30 ft, Width = W (unknown), Diagonal = 76 ft.
Using the Pythagorean theorem: W = sqrt(76^2 - 30^2)
4. Circle Screen:
Given: Diagonal = 76 ft.
Radius (r) = Diagonal / 2 = 76 / 2
5. Ellipse Screen:
Given: Height = 30 ft, Width = W (unknown), Diagonal = 76 ft.
Using the Pythagorean theorem: W = sqrt(76^2 - 30^2)
To calculate the missing measurement for each of the 6 types of screens (width, height, or diagonal), we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the width, height, and diagonal as the sides of a right triangle. So, we can use the Pythagorean theorem to calculate the missing measurement.
Let's calculate the missing measurements for each type of screen:
1. Missing width:
We know the height (30 ft.) and the diagonal. Let's represent the width as "x". Using the Pythagorean theorem, we have the equation:
x^2 = diagonal^2 - height^2
x^2 = 76^2 - 30^2
x^2 = 5776 - 900
x^2 = 4876
x ≈ √4876
x ≈ 69.8 ft.
2. Missing height:
We know the width and the diagonal. Let's represent the height as "y". Using the Pythagorean theorem, we have the equation:
y^2 = diagonal^2 - width^2
y^2 = 76^2 - (69.8)^2
y^2 = 5776 - 4860.04
y^2 = 916.96
y ≈ √916.96
y ≈ 30.3 ft.
3. Missing diagonal:
We know the width and height. Let's represent the diagonal as "d". Using the Pythagorean theorem, we have the equation:
d^2 = width^2 + height^2
d^2 = (69.8)^2 + (30)^2
d^2 = 4860.04 + 900
d^2 = 5760.04
d ≈ √5760.04
d ≈ 75.9 ft.
By using the Pythagorean theorem, we have calculated the missing width, height, and diagonal for each type of screen.