Question

If the ratio of the height of a tower and the length of its shadow is √3 :1, then the angle of elevation of the Sun is 30º. Is it true or false?

Answer 1

Answer is False.

Let the height of tower, AB = h m

The length of shadow, BC = x m

According to given question,

\(\frac{AB}{BC} = \frac {\sqrt 3}1\)

\(\frac hx = \frac{\sqrt 3}1\)

We know that,

In ΔABC,

\(\frac{AB}{BC} = \tan \theta\)

\(\tan \theta = \frac hx\)

\(\tan \theta = \frac {\sqrt 3}1\)

\(\tan \theta = {\sqrt 3}\)

\(\tan \theta = \tan 60° \)

\(\theta = 60°\)

Hence, the angle of elevation is 60°.

Answer 2

Solution is......