Question

Two ships are sailing in the sea on the two sides of a lighthouse The angles of elevation of the top of the lighthouse as observed from the two
ships are ${30}^0$ and ${45}^0$ respectively If the lighthouse is $100$ m high the distance between the two ships is

• A. $173$m
• B. $200$m
• C. $273$m
• D. $300$m

Answer 1

The correct option is C $273$m

Let $AB$ be the height of lighthouse and $C$ and $D$ be the position of the ships.

Given $AB=100$ m and $\angle ACB={30}^0$$\angle ADB={45}^0$

In $\Delta BCA$

$\frac{AB}{AC}=tan{30}^0=\frac{1}{\sqrt{3}}$

$\Rightarrow AC=\sqrt{3}AB=100\sqrt{3}$

In $\Delta BAD$

$\frac{AB}{AD}=tan{45}^0=1$

$\Rightarrow AD=AB=100m$

$\therefore CD=AC+AD=100\sqrt{3}+100=100(\sqrt{3}+1)=100(1.73+1)=273m$