Question

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

• A. $12$ m
• B. $10$ m
• C. $8$ m
• D. $6$ m

Answer 1

The correct option is A $12$ m

Given that : Heights of two poles are $20$ and $14$m respectively.

Angle wire makes with horizontal $={30}^{\circ }$

Let distance between two poles be $x$ and length of wire be $y$

$tan{30}^{\circ }=\frac{20-14}{x}=\frac{6}{x}$

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

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

As length of the wire will form the hypotenuse of right angled triangle thus formed,

$y^2=6^2+(6\sqrt{3}{)}^2=144$

$\therefore y=12$ m