# A Man in a Boat Rowing Away from a Lighthouse 100 M High Takes 2 Minutes to Change the Angle of Elevation of the Top of the Lighthouse from 60° to 30°. Find the Speed of the Boat in Metres per Minute - Mathematics

Sum

A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute [Use sqrt3 = 1.732]

#### Solution

AB is a lighthouse of height 100m. Let the speed of boat be x metres per minute. And CD is the distance which man travelled to change the angle of elevation.

Therefore,
CD = 2x [Distance = speed x time]

tan(60°) = ("AB")/("BC")

sqrt3 = 100/"BC"

=> "BC" = 100/sqrt3

tan(30°) = "AB"/"BD"

=> 1/sqrt3 = 100/"BD"

BD = 100sqrt3

CD = BD - BC

2"x" = 100 sqrt3 - 100/sqrt3

2"x" = (300 - 100)/sqrt3

=> "x" = 200/(2sqrt3)

=> x = 100/sqrt3

Using,

sqrt3 = 1.73

"x" = 100/1.73 = 57.80

Hence, the speed of the boat is 57.80 metres per minute.

Concept: Trigonometry
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