Question

The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. What is the length of the wire?

• A. 6 m
• B. 10 m
• C. 8 m
• D. 12 m

Answer 1

The correct option is D

12 m

In triangle ABC,
BC = y = 20 - 14 = 6m

Let AB = $x$

$\Rightarrow \text{sin}{30}^{\circ }$= $\frac{BC}{AB}$

$\Rightarrow$ $\frac{1}{2}$ = $\frac{6}{x}$

$\Rightarrow$ $x$ = 12

Thus, the length of the string is 12 m.