Question

At a certain instant, the length of the shadow of a pillar and its height are in the ratio 3 :1 . What is the angle of elevation at that instant

Answer 1

Answer:

the angle is elevation is $30^\circ$

Step-by-step explanation:

Let the common ratio is x

Then

The length of the shadow = \sqrt{3}x

Height of the pillar = x

Let A be the point till where the shadow is formed and if BC is the pillar then ABC will be a right angled triangle

AB will be the length of the shadow = \sqrt{3}x

BC will be the height of pillar = x

Thus

$\tanA=\frac{BC}{AB}$

$\implies\tanA=\frac{x}{\sqrt{3}x}$

$\implies\tanA=\frac{1}{\sqrt{3}}$

$\implies\tanA=\tan30^\circ$

$\implies A=30^\circ$

Therefore the angle is elevation is $30^\circ$

Note: The ratio should be $\sqrt{3}:1$ if this is a secondary school level question.

Hope this helps.