Question

A man is standing on the deck of a ship, which $8m$ above water level. He observe the angle of elevation of top of hill as ${60}^o$ and the angle depression of the base of the hill as ${30}^o$. Calculate the distance of the hill from the ship and the height of the hill.

Answer 1

R.E.F.Image

$tan60=\frac{x}{y}$

$\sqrt{3}=\frac{x}{y}$

$y=\frac{x}{\sqrt{3}}\cdots \left(1\right)$

$tan30=\frac{8}{y}$

$\frac{1}{\sqrt{3}}=\frac{8}{y}$

$y=8\sqrt{3}\cdots \left(2\right)$

(2) in (1)

$8\sqrt{3}=\frac{x}{\sqrt{3}}$

$x=24$

height of hill $8+x$

$=8+24$

$=32m$

distance from ship to hill $=8\sqrt{3}m$