A straight, tight wire 18 m long runs from the top of a vertical pole to a peg fixed in the level ground. The wire makes an angle of \(60^\circ\) with the ground. How tall is the pole?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(9\sqrt{3}\) m
The wire, the ground and the pole form a right-angled triangle with the wire as the hypotenuse. The height of the pole is the side opposite the \(60^\circ\) angle, so it is found with the sine.
\(\sin 60^\circ=\displaystyle\frac{\text{height}}{18}\)
Height \(=18\times\displaystyle\frac{\sqrt{3}}{2}=9\sqrt{3}\) m
