Question

From a boat $300$ metres away from a vertical cliff, the angles of elevation of the top and the foot of a vertical concrete pillar at the edge of the cliff are ${55}^{\circ }{40}^{\prime }$ and ${54}^{\circ }{20}^{\prime }$ respectively. Find the height of the pillar correct to the nearest metre.

Answer 1

Let the height of the cliff be $h$ metres
and the height of the pillar is $x$ metres.

Then, in $△BDC,$

$\tan {54}^{\circ }{20}^{\prime }=\frac{BD}{BC}$

$\Rightarrow \tan {54}^{\circ }{20}^{\prime }=\frac{h}{300}$

$\Rightarrow 1.37=\frac{h}{300}$

$\Rightarrow h=411m$

Now in $△ABC,$

$\tan {55}^0{40}^{\prime }=\frac{x+h}{300}$

$\Rightarrow 1.42=\frac{x+411}{300}$

$\Rightarrow 426=x+411$

$\Rightarrow x=15$

Height of pillar $=15m$