First slide

Applications of trigonometry

Question

The angle of elevation of an object from a point P on the level ground is $α$ . Moving d meters on the ground towards the object, the angle of elevation is found to be $β$ . Then the height (in meters) of the object is

Easy

A

$d . \tan α$
B

$d . c o t β$
C

$\frac{d}{\cot α + \cot β}$
D

$\frac{d}{\cot α - \cot β}$

Solution

$\tan α = \frac{h}{x + d} \Rightarrow x + d = h \cot α$
$\begin{array}{l} \tan β = \frac{h}{x} \Rightarrow x = h \cot β \\ ∴ x + d - x = h [\cot α - \cot β] \\ \Rightarrow h = \frac{d}{\cot α - \cot β} \end{array}$

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