Question

From a light house the angle of depression of two ships on opposite sides of the light house are observed to be ${30}^o$ and ${45}^o$. If the height of the light house be $100$ metres, find the distance between the ships if the line joining them passes through the foot of the light house.

Answer 1

(Refer to Image)

Height of light house= $AB=100m$

Let $BC=x$ $m$ & $BD=y$ $m$

In ${△}^{le}ABC$,

$\tan {30}^o=\frac{AB}{BC}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{100}{x}$

$\Rightarrow x=100\sqrt{3}m$

In ${△}^{le}ABD$,

$\tan {45}^o=\frac{AB}{BD}\Rightarrow 1=\frac{1000}{y}\Rightarrow y=100m$

$\Rightarrow x+y=100\sqrt{3}+100m=100(\sqrt{3}+1)m$

$=273.2051$ m