Question

A rope of length $5$ metres is tightly tied with one end at the top of a vertical pole and other end to the horizontal ground. If the rope makes an angle ${30}^0$ to the horizontal, then the height of the pole is

• A. $\frac{5}{2}$m
• B. $\frac{5}{\sqrt{2}}$m
• C. $5\sqrt{2}$m
• D. $5$ m

Answer 1

The correct option is A $\frac{5}{2}$m

Consider the above given triangle
Let $OP=h$ be the height of the vertical pole
Let $HP$ be the length of the rope
angle $PHO={30}^0$ .......(given)
Therefore, $\sin {30}^0=\frac{OP}{HP}=\frac{h}{5}$
$\Rightarrow \frac{1}{2}=\frac{h}{5}$
$\Rightarrow h=\frac{5}{2}$
Answer is $\frac{5}{2}$ metre.