Question

A man on the deck of a ship is $12m$ above water level. he observes that the angle of elevation, of the top of a cliff is ${45}^o$ and the angle of depression of its base is ${30}^o$. Calculate the distance of the cliff from the ship and the height of the cliff.

• A. Height$=36m$; Distance$=29m$
• B. Height$=46.256m$; Distance$13.759m$
• C. Height$=40m$; Distance$=25m$
• D. Height$=32.784m$; Distance$=20.784m$

Answer 1

The correct option is D Height$=32.784m$; Distance$=20.784m$

Let the distance of the cliff from the ship be x.
Let the height of the cliff be y.
Hence
$\tan {45}^0=1=\frac{h-12}{y}$
Hence
$h-12=y$ Or
$h=y+12$ ...(i)
And
$\tan {30}^0=\frac{12}{y}=\frac{1}{\sqrt{3}}$
Hence
$y=12\sqrt{3}$
$=20.784m$
Now
$h=y+12$
$=20.784+12$
$=32.784m$