First slide

Applications of trigonometry

Question

A flag staff stands upon the top of a building. At a distance d meters the angles of elevation of the tops of the flag staff and building are $α$ and $β$ respectively. The height of the flag staff is

Easy

A

$d (\tan α + \tan β) m t$
B

$d (\tan α - \tan β) m t$
C

$d (\sin α + \sin β) m t$
D

$d (\sin α - \sin β) m t$

Solution

$W e h a v e \tan β = \frac{x}{d} \Rightarrow x = d \tan β$
$A l s o \tan α = \frac{h + x}{d} \Rightarrow h + x = d \tan α$
$\Rightarrow h + d \tan β = d \tan α \Rightarrow h = d (\tan α - \tan β)$

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