Question

Hans is sitting in a movie theater, 19 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 15°, and the angle of depression from his line of sight to the bottom of the screen is 22°. Find the height of the entire screen. Do not round any intermediate computations. Round your answer to the nearest tenth.

Answer 1

12.8 m

Explanation:

From the diagram :

Height PR = 19m

Using Pythagoras :

From triangle PQR:

QR = x

Tan θ = opposite / Adjacent

Tan 22° = x / 19

x = tan 22° * 19

x = 0.4040262 * 19

x = 7.6764982 m

From triangle PRS:

SR = y

Tan θ = opposite / Adjacent

Tan 15° = y / 19

y = tan 15° * 19

y = 0.2679491 * 19

y = 5.0910346

Height of entire screen :

(7.6764982 + 5.0910346) m

= 12.7675328 m

= 12.8 m