Question

if a tower 30m high casts a shadow 10 root3 m long on the ground. then what is the angle of elevation of the sun?

Answer 1

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Answer 2

Answer:

The angle of elevation of the sun is 60°.      

Step-by-step explanation:

Given : If a tower 30 m high casts a shadow $10\sqrt{3}$ m long on the ground.

To find : What is the angle of elevation of the sun?

Solution :

Let the position of sun is at 'A'.

According to question a right angle triangle is form $\triangle ABC$

Refer the attached figure below.

With AB as height of the tower AB=30 m

and BC is the base where shadow cast $BC=10\sqrt{3}$

Let $\theta$ be the angle of elevation.

Applying trigonometry property,

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

$\tan\theta=\frac{30}{10\sqrt3}$

$\tan\theta=\frac{3}{\sqrt3}$

$\tan\theta=\sqrt3$

$\theta=\tan^{-1}(\sqrt3)$

$\theta=\frac{\pi}{3}$

$\theta=60^\circ$

Therefore, The angle of elevation of the sun is 60°.