Question

Goran is sitting in a movie theater, 5 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 18, and the angle of depression from his line of sight to the bottom of the screen is 48. Find the height of the entire screen.

Answer 1

Approximately

Height of screen= 7.1 meters

Explanation:

Angle of elevation= 18°

Angle of depression= 58°

Distance of Goran from screen= 5 m

Height of screen from the attachment below

X+y

First let's determine angle a and b

a= 180-90-18

a= 72°

b= 180-90-48

b= 43°

Using sine formula

5/sin a= x/sin 18

5/sin 72= x/sin18

(5*sin 18)/sin 72= x

1.6246 = x

X= 1.6246 m

Y/sin 48= 5/sin b

Y= (5*sin 48)/sin 43

Y= (5*1.08965779)

Y= 5.4483 m

Height of screen= x+y

Height of screen= 1.6246+5.4483

Height of screen= 7.0729

Approximately

Height of screen= 7.1 meters