The tops of two poles of height 38 m and 56 m are connected by a cable. If the cable makes an angle of 30° with the horizontal, then the distance between the bases of the poles is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(18\sqrt{3}\) m
A horizontal line from the top of the shorter pole to the taller pole makes a right triangle with the cable: the vertical side is the difference in heights, and the horizontal side equals the distance \(d\) between the bases. In it, \(\tan30^\circ=\frac{\text{vertical side}}{\text{horizontal side}}\).
Vertical side \(=56-38=18\) m
\(\displaystyle \tan30^\circ=\frac{18}{d}\), and \(\tan30^\circ=\frac{1}{\sqrt{3}}\)
\(d=18\sqrt{3}\) m