Question

The tops of two poles of heights 18 metres and 12 metres are connected by a rope. If the rope makes an angle ${30}^0$ with the horizontal, the length of the rope in metres is

• A. $12$
• B. $18$
• C. $24$
• D. $30$

Answer 1

Answer: (A)

$12$

According to the problem given ,

Height of the first pole $=AB=18m$

Height of the second pole $=CD=12m$

Length of the wire $=AD$

$AE=AB-BE$

$=AB-CD$

$=18-12$

$AE=6m$

In $\Delta AED,$

$\angle AED=90°,$

$\angle ADE=30°$ ( given )

$\sin 30°=\frac{AE}{AD}$

$\frac{1}{2}=\frac{6}{AD}$

$AD=6\times 2$

$AD=12m$

Therefore ,

Length of the wire $=AD=12m$

Option ( a ) is correct.