A pole casts a shadow of length \(2\sqrt{3}\) meter on the ground when the sun's elevation is 60°. The height of the pole is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 meter
The pole AB, its shadow BC and the sun’s ray AC form a right triangle with the right angle at B, the foot of the pole. The sun’s elevation is the angle at C, the tip of the shadow, and in this triangle \(\tan\theta=\frac{\text{height}}{\text{shadow}}\).
In the right triangle ABC: \(\tan60^\circ=\displaystyle\frac{h}{2\sqrt{3}}\), where \(\tan60^\circ=\sqrt{3}\)
Height of the pole: \(h=2\sqrt{3}\times\sqrt{3}=2\times3=6\) m