First slide

Applications of trigonometry

Question

The angles of elevation measured from two points A and B on a horizontal line from the foot of a tower are $α$ and $β$ . If AB=d, then the height of the tower is

Easy

A

$|\frac{d \sin α \sin β}{\sin (α - β)}|$
B

$|\frac{d \sin α \sin β}{\sin (α + β)}|$
C

$|\frac{d \sin α + \sin β}{\sin (α - β)}|$
D

$|\frac{d \sin α - \sin β}{\sin (α - β)}|$

Solution

$\tan β = \frac{h}{x} \Rightarrow x = h \cot β$
$\tan α = \frac{h}{x + d} \Rightarrow x + d = h \cot α \Rightarrow h \cot β + d = h \cot α$
$\Rightarrow h = \frac{d}{\cot α - \cot β} = \frac{d . \sin α \sin β}{\sin (β - α)}$

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