Question

Statement (1): At a particular time, the length of the shadow of a 50 m tower is `50sqrt3` m.

Statement (2): The sun’s altitude is 30°.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

Using the tangent ratio for a tower of height 50 m and sun's altitude (angle of elevation) of 30°:

\[\text{Shadow length} = \frac{50}{\tan 30^\circ} = 50\sqrt{3}\text{ m}\]

Thus, both Statement 1 and Statement 2 are true, and Statement 2 correctly explains Statement 1.