Question

A person is standing at a distance of 50 m from a temple looking at its top. The angle of elevation is $45^\circ$. Find the height of the temple.

Hint:

When the angle of elevation is $45^\circ$, the height and base are equal in right-angled triangle problems.

Answer 1

Step 1: Understand the situation.
Let the height of the temple be $h$ m and the distance from the person to the temple be 50 m. The angle of elevation is $45^\circ$.
Step 2: Apply the tangent trigonometric ratio.
\[ \tan \theta = \frac{\text{opposite side}}{\text{adjacent side}} \] \[ \tan 45^\circ = \frac{h}{50} \] Step 3: Simplify.
\[ 1 = \frac{h}{50} \Rightarrow h = 50 \] Step 4: Conclusion.
Therefore, the height of the temple is 50 m.
Correct Answer: 50 m