Question

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are ${30}^o$ and ${45}^o$ 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 lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, $\angle ACB={30}^o,\angle ADB={45}^o$

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

$AC=AB\times \sqrt{3}=100\sqrt{3}m$

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

$AD=AB=100m$

Therefore,

$CD=AC+AD=(100\sqrt{3}+100)m$

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

$=100\times 2.73m$

$=273m$