First slide

Applications of trigonometry

Question

A vertical pole stands at a point A on the boundary of a circular park of radius ‘a’ and subtends an angle $β$ at another point B on the boundary. If the chord AB subtends an angle $α$ at the center of the park, the height of the pole is

Moderate

A

$2 asin \frac{α}{2} \tan β$
B

$2 acos \frac{α}{2} \tan β$
C

$2 a \sin \frac{α}{2} \cot β$
D

$2 acos \frac{α}{2} \cot β$

Solution

$S u p p o s e t h a t h b e t h e h e i g h t o f t h e p o l e$
$from triangle APB, \tan β = \frac{h}{AB} \Rightarrow h = ABtan β$
$from triangle ABC, \sin \frac{α}{2} = \frac{AB}{2 a} \Rightarrow AB = 2 asin \frac{α}{2}$
$∴ h = 2 asin \frac{α}{2} \tan β$

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