Question

The angle of elevation of the top of a lamp-post as observed from a point $40m$ distant from the foot of the post, is ${30}^0.$ The height of the lamp post is

• A. $40\sqrt{3}$m
• B. $\frac{40\sqrt{3}}{3}$m
• C. $20m$
• D. $\frac{40\sqrt{3}}{2}$

Answer 1

Answer: (B)

$\frac{40\sqrt{3}}{3}$m

Consider the given triangle

Let AB be the height of the lamp post denoted by h

Let BC bet the horizontal distance of the point from the foot of the lamp post

Given that angle $C={30}^0$

Therefore

$\tan {30}^0=\frac{1}{\sqrt{3}}$

$=\frac{AB}{BC}$

$=\frac{h}{40}$

$h=\frac{40}{\sqrt{3}}$

Rationalising the denominator we get

$h=\frac{40\sqrt{3}}{3}$

Hence answer is B