The tops of two poles of height 22 m and 31 m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire (in m) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(6\sqrt{3}\)
A horizontal line through the top of the shorter pole makes a right triangle with the wire as its hypotenuse. The vertical side is the difference of the heights, and it lies opposite the 60° angle, so \(\sin60^\circ=\frac{\text{rise}}{\text{wire}}\).
Rise \(=31-22=9\) m
\(\displaystyle \sin60^\circ=\frac{9}{L}\), so \(\displaystyle \frac{\sqrt{3}}{2}=\frac{9}{L}\)
\(\displaystyle L=\frac{18}{\sqrt{3}}=6\sqrt{3}\) m