If the height of a pole is 9 m and the angle of elevation of the sun is 60°, then what is the length of its shadow (in m)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(3\sqrt{3}\)
The pole, its shadow and the sun's ray from the top of the pole form a right triangle, with the angle of elevation at the tip of the shadow. Opposite that angle is the pole and beside it is the shadow, so \(\tan 60^\circ=\frac{\text{pole}}{\text{shadow}}\).
\(\tan 60^\circ=\sqrt{3}=\frac{9}{BC}\)
\(BC=\frac{9}{\sqrt{3}}=\frac{9\sqrt{3}}{3}=3\sqrt{3}\) m