Question

The tops of two poles of height 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree 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 12m.