Question

A man in a boat rowing away from a lighthouse 150m high,takes 2 minutes to change the angle of elevation of the top of the lighthouse from 45 to 30 degree. Find the speed of the boat.

Answer 1

Step-by-step explanation:

h = 150 m => (opposite side)

let x be the distance of the boat from the light house at the first instance

let y be the distance moved by the boat in 2 minutes

tan 45° = 150/x => 1 = 150/x => x = 150 m

again, tan 30° = 150/(x+y) => 1/√3 = 150/(x+y)

x+y = 150√3

150 + y = 150√3

y = 150√3 - 150 => 150(√3-1) => 150 × 0.73

=> 109.5 m

therefore the boat covered 109.5 m in 2 minutes

now, speed = distance/time

=> speed = 109.5/2

=> 54.75 m/min

=> 3.285 km/hr