Question

Projector sizes are based on the length of the diagonal of the projector’s rectangular screen. If a 150-inch projector’s diagonal forms a 37° angle with the base of the screen, what is the vertical height of the screen to the nearest inch?

A) 110 in.
B) 85 in.
C) 120 in.
D) 90 in.

Answer 1

Using the trigonometric sine function and the given 37° angle and 150-inch diagonal of a projector screen, the vertical height is calculated to be approximately 90 inches.

Step-by-step explanation:

To find the vertical height of the screen in a projector where the screen diagonal is 150 inches and forms a 37° angle with the base, we can use trigonometric functions. Specifically, the sine function relates the opposite side (the vertical height we want to find) to the hypotenuse (the diagonal of the screen) in a right-angled triangle. The function is as follows:

sin(37°) = (vertical height) / (diagonal length)

We can isolate the vertical height and calculate its value:

vertical height = sin(37°) × diagonal length
vertical height = sin(37°) × 150 inches

Using a calculator, we find that:

vertical height ≈ 90 inches

Therefore, the vertical height of the screen to the nearest inch is 90 inches, which corresponds to option D.