Question

It is observed that the top of an electric pole is at an angle of elevation of $45^\circ$. The observation point is 8 meters away from the foot of the pole. What is the height of the electric pole?

• A. 8 m
• B. $8\sqrt{3}$ m
• C. 16 m
• D. $4\sqrt{3}$ m

Hint:

If angle of elevation is $45^\circ$, then height = base.

Answer 1

The Correct Option is A

Concept: In a right-angled triangle, for an angle of elevation: \[ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} \] Here: Opposite side = height of pole = $h$ Adjacent side = distance from observer = $8$ m Angle = $45^\circ$

Step 1: Apply tangent ratio \[ \tan 45^\circ = \frac{h}{8} \]

Step 2: Substitute value \[ 1 = \frac{h}{8} \]

Step 3: Solve \[ h = 8 \text{ m} \] Conclusion: The height of the electric pole is $8$ m.