Question

If a flagstaff of 6 meters height placed on the top of a tower throws a shadow of 2v3 meters along the ground,then find the angle that the sun makes with the ground.

Answer 1

Please check the attachments. Thank you.

Answer 2

Angle that the sun makes with the ground is $\bold {60^{\circ}}$

Given:

Length of the flagstaff = 6m

Length of the shadow $=2 \sqrt{3} \mathrm{m}$

To find:  

The angle that the sun makes with the ground.

Solution:

Let’s refer to this figure given below:  

We know that formula for calculating $\tan \theta$ with respect to right angled triangle is,

$\tan \theta=\frac{\text {opposite side}}{\text {adjacent side}}$

Now, from the figure, it is clear that,

$\begin{array}{l}{\tan \theta=\frac{6}{2 \sqrt{3}}} \\ {=\frac{3}{\sqrt{3}}}\end{array}$

$=\frac{\sqrt{3} \times \sqrt{3}}{\sqrt{3}}$ [∵3 can be written as $\sqrt{3} \times \sqrt{3}$]

We know that the value of tan$\sqrt{3}=60^{\circ}\Rightarrow \tan \theta=60^{\circ}$

$=\sqrt{3}$