A man on a lighthouse that stands 50 meters tall is observing a boat moving away from it. Over the course of 10 seconds, the angle of depression to the boat shifts from 60° to 30°. What is the approximate speed of the boat?
Show answer & explanation
Correct answer: B
Explanation
Height of the lighthouse = 50 meters
tan 60° = 50 / x
x = 50/√3 meters
After 10 seconds -
tan 30° = 50 / y
y = 50√3 meters
Distance covered by the boat = y − x
= 50√3 − 50/√3 = 100/√3
≈ 57.7 meters
Speed = 57.7 ÷ 10
≈ 5.8 meters/second