Question

A boy observed the top of an electric pole at an angle of elevation of \(60^\circ\) when the observation point is 6 meters away from the foot of the pole, then the height of the pole is:

• A. 6 m
• B. \(6\sqrt{2}\) m
• C. \(6\sqrt{3}\) m
• D. \(6/\sqrt{3}\) m

Hint:

To find the height of an object using the angle of elevation, use the tangent function: \(\tan(\theta) = \frac{\text{height}}{\text{distance}}\).

Answer 1

The Correct Option is B

We can use the formula for the tangent of an angle in a right triangle: \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \] Here, \(\theta = 60^\circ\), the adjacent side is the distance from the foot of the pole, which is 6 meters, and the opposite side is the height of the pole \(h\). Therefore: \[ \tan 60^\circ = \frac{h}{6} \] Since \(\tan 60^\circ = \sqrt{3}\), we have: \[ \sqrt{3} = \frac{h}{6} \quad \Rightarrow \quad h = 6\sqrt{3} \, \text{m} \] Thus, the correct answer is option (3).