Question

scott is sitting in a movie theater, 21 meters from the screen. the angle of elevation from his line of sight to the top of the screen is 17°, and the angle of depression from his line of sight to the bottom of the screen is 38°. find the height of the entire screen. do not round any intermediate computations. round your answer to the nearest tenth. note that the figure below is not drawn to scale.

Explanation:

Step1: Find upper - part height

Let the height from the horizontal line of sight to the top of the screen be $h_1$. Using tangent function, $\tan(17^{\circ})=\frac{h_1}{21}$, so $h_1 = 21\times\tan(17^{\circ})$.

Step2: Find lower - part height

Let the height from the horizontal line of sight to the bottom of the screen be $h_2$. Using tangent function, $\tan(38^{\circ})=\frac{h_2}{21}$, so $h_2 = 21\times\tan(38^{\circ})$.

Step3: Find total height

The total height $H$ of the screen is $H=h_1 + h_2=21\times\tan(17^{\circ})+21\times\tan(38^{\circ})$.
$H = 21\times(\tan(17^{\circ})+\tan(38^{\circ}))\approx21\times(0.3057 + 0.7813)=21\times1.087\approx22.8$.

Answer:

$22.8$ meters