Question

From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be \( 45^\circ \). The height (in metres) of the tower is :

• A. \( 10\sqrt{3} \)
• B. \( 30\sqrt{3} \)
• C. \( 60 \)
• D. \( 30 \)

Hint:

Whenever the angle of elevation is \( 45^\circ \), the height is always equal to the distance from the base.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is an application of basic trigonometry using the tangent ratio in a right-angled triangle.
Step 2: Detailed Explanation:
Let \( h \) be the height and \( d \) be the distance (60 m).
\( \tan 45^\circ = \frac{\text{Height}}{\text{Distance}} \).
We know \( \tan 45^\circ = 1 \).
\[ 1 = \frac{h}{60} \implies h = 60 \text{ m} \]
Step 3: Final Answer:
The height of the tower is 60 m.