Question

There are 2 ships on either side of a lighthouse. If the angles of elevation of the lighthouse from both the ships are ${30}^{\circ }$ and ${45}^{\circ }$ respectively. If the height of lighthouse is 'h' and distance between the two ships is 'd', the ratio of 'd' to 'h' up to 1 decimal place is ___

Answer 1

In ΔADB, tan${45}^{\circ }$ = $\frac{h}{BD}$ $\Rightarrow$ BD = h

In ΔADC, tan${30}^{\circ }$ = $\frac{h}{DC}$ $\Rightarrow$ DC = h$\sqrt{3}$

BD + DC = BC $\Rightarrow$ h +h$\sqrt{3}$ = d

$\frac{d}{h}$ = 1 + $\sqrt{3}$ = 2.7 (upto 1 decimal place)