An observer 2 m tall is 30 m away from a roof. The angle of elevation of the top of the roof from his eye is 45°. What is the height of the roof?
Show answer & explanation
Correct answer: B
Explanation
Observer's height = 2 meters
Distance from the roof = 30 meters
Angle of elevation = 45°
tanθ = (Difference in height) / Distance
tan45° = (H − 2)/30
⇒ 1 = (H − 2)/30
⇒ H − 2 = 30
⇒ H = 32 meters