Class 10

Math

All topics

Some Applications of Trigonometry

A lamp post standing at a point $A$ on a circular path of radius $r$ subtends an angle $α$ at some point $B$ on the path, and $AB$ subtends an angle of $45_{0}$ at any other point on the path, the height of the lamp post is

- $2 rcotα$
- $2 r tanα$
- $2 rtanα$
- $2 r cotα$

Therefore it subtends an angle of $90_{o}$ at the center.

$∴AB=r_{2}+r_{2} $

$=r2 $

$tanα=ABh $

$tanα=r2 h $

$⇒h=r2 tanα$

$∴AB=r_{2}+r_{2} $

$=r2 $

$tanα=ABh $

$tanα=r2 h $

$⇒h=r2 tanα$