Question

The height of a light house is $85m.$ An observer on it found the angle of depression to a boat to be ${30}^{\circ },$ which was sailing towards the light house. After $2$ minutes, the angle of depression for the same boat was ${60}^{\circ }.$ What was the speed of the boat in $km/hr$ ? $(\sqrt{3}=1.7)$

Answer 1

R.E.F image

$l\left|\right|$BD hence the angles

In the figure,tan30=AB=1=AB

BD $\sqrt{3}BD$

$\Rightarrow BD=\sqrt{3}AD$

Also tan60$=\frac{AB}{BC}=\sqrt{3}=\frac{AB}{BC}$

$\Rightarrow BC=\frac{1}{\sqrt{3}}AB$

$\Rightarrow CD=BD=BC=AB(\sqrt{3}-\frac{1}{\sqrt{3}})=\frac{2AB}{\sqrt{3}}=\frac{2}{\sqrt{3}}\times 85=\frac{170}{\sqrt{3}}$

$\Rightarrow Sspeed=\frac{Distance}{Time}=\frac{170}{\sqrt{3}10}\times \frac{60}{2\times 10}=3km/hr$