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 = 100`sqrt3`

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.