First slide

Applications of trigonometry

Question

The angles of elevation of the top of a tower from two points distant ‘a’ and ‘b’ from the base and in the same straight line with it are complementary. The height of the tower is

Easy

A

$a b$
B

$\sqrt{a b}$
C

$\frac{a}{b}$
D

$\sqrt{\frac{a}{b}}$

Solution

$W e h a v e \tan α = \frac{h}{a}, \tan (90 - α) = \frac{h}{b}$
$\Rightarrow \cot α = \frac{h}{b} \Rightarrow \frac{a}{h} = \frac{h}{b}$
$\Rightarrow h^{2} = a b \Rightarrow h = \sqrt{a b}$

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