Question

The length of the shadow of a tree is $\sqrt{3}$ times its height, then find the angle of elevation of the sun at the same time.

Answer 1

R.E.F image

Let AC be tree and AB be its shadow.

Given: AB =$\sqrt{3}h$ ---(1)

then,

In $△ABC$,

$\frac{AC}{AB}=tan\theta$

$\frac{h}{\sqrt{3}h}=tan\theta$

$tan\theta =\frac{1}{\sqrt{3}}\Rightarrow [\theta ={30}^{\circ }]$

$\therefore$ Angle of elevation of sun is ${30}^{\circ }$