Question

The height of a light house is 85 m. An observer on it found the
angle of depression to a boat to be 30°, which was sailing towards
the light house. After 2 minutes, the angle of depression for the same
boat was 60°. What was the speed of the boat in km/hr ? (V3 = 1.7)​

Answer 1

The speed of the boat is 3 Km/hr.

Step-by-step explanation:

In the figure, tan(30) = AB=1=AB

BD √3 BD

BD = √3 AD

Also tan(60) = AB / BC = √3 = AB / BC

BC= 1/√3 AB

CD = BD = BC= AB( 3 − 1 /√3) = 2AB / √3

= 2 /√3 x 85 = 170 / √3

Speed = Distance / Time = 170 / √3 x 60 2 x 10

= 3 Km/hr