Question

The tops of two poles of height 20m and 14m are connected by a wire. If the wire makes an angle of 30 degrees with horizontal, then the length of the wire is:

• A. 6m
• B. 10m
• C. 8m
• D. 12m

Answer 1

The correct option is D

12m

In triangle ABC,

BC = y = 20-14 = 6m; AC = x

$\Rightarrow tan{30}^{\circ }=\frac{y}{x}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{6}{x}$

$\Rightarrow x=6\sqrt{3}$

Now, the length of rope AB is given by:

$A{C}^2+B{C}^2=A{B}^2$

$\Rightarrow AB=12m$
Thus, the length of the string is 12 m.