Question

A hill slopes upwards at an angle of ${30}^{\circ }$ with ground. If he walks 100 m and reaches the top of the hill, calculate the height of the hill.

• A. 30 m
• B. 40 m
• C. 50 m
• D. 60 m

Answer 1

The correct option is C 50 m


Let $h$ be the height of the hill.
Distance he walked through the slope = 100 m

The trigonometric ratio connecting the opposite side and hypotenuse is $sin\theta$.
Angle of elevation = ${30}^o$

Hence, $sin{30}^{\circ }=\frac{BC}{AB}=\frac{h}{100}$
We know that, $sin{30}^{\circ }=\frac{1}{2}$
Then, $\frac{1}{2}=\frac{h}{100}$
$\Rightarrow h=\frac{1}{2}\times 100=50m$

So, height of the hill = 50 m.