Question

The ratio of the length of a vertical pole and length of its shadow on the horizontal surface is \(3: \sqrt{3}\).

Assertion (A): The angle of elevation of the sun is 60°.

Reason (R): If angle of elevation of the sun is \[\theta, \tan \theta=\frac{3}{\sqrt{3}}=\sqrt{3}=\tan 60^{\circ}\]

पर्याय

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given, the ratio of the height of a vertical pole to the length of its shadow is \(3: \sqrt{3}\)

Let AB be the pole and BC be the shadow and angle of elevation of Sun be θ.

\[\Rightarrow \frac{\text{Height of a vertical pole}}{\text{Height of shadow}} = \frac{3}{\sqrt{3}}\]

\[\Rightarrow \frac{AB}{BC} = \sqrt{3}\]

\[\Rightarrow \tan \theta = \sqrt{3}\]

\[\Rightarrow \tan \theta = \tan 60^\circ\]

\[\Rightarrow \theta = 60^\circ\]

∴ Both A and R are true and R is correct reason for A.