First slide

Applications of trigonometry

Question

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. The height of the hill is

Easy

A

$\frac{h \cot p}{\cot p - \cot q}$
B

$\frac{h \cot q}{\cot p - \cot q}$
C

$\frac{h \cot p}{\cot p + \cot q}$
D

$\frac{h \cot q}{\cot p + \cot q}$

Solution

We have $\tan q = \frac{x}{d} \Rightarrow d = x \cot q, \tan p = \frac{x - h}{d} \Rightarrow d = (x - h) \cot p$
$\Rightarrow x \cot q = (x - h) \cot p$
$\Rightarrow x \cot p - x \cot q = h \cot p$
$\Rightarrow x = \frac{h \cot p}{\cot p - \cot q}$

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