First slide

Applications of trigonometry

Question

From the top of a light house, the angles of depression of two stations on opposite side of it at a distance ‘a’ apart are $α$ and $β$ . The height of the light house is

Easy

A

$\frac{a}{\sin α + \sin β}$
B

$\frac{a}{\cos α + \cos β}$
C

$\frac{a}{\tan α + \tan β}$
D

$\frac{a}{\cot α + \cot β}$

Solution

$\tan α = \frac{h}{x} \Rightarrow x = h \cot α$ , $\tan β = \frac{h}{a - x} \Rightarrow a - x = h \cot β$
$∴ a - h \cot α = h \cot β$ $\Rightarrow h = \frac{a}{\cot α + \cot β}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App