Question

The string of a flying kite is tied to a point on the ground. The length of the string between the kite and the point on the ground is 80 m. The string makes an angle of $30^\circ$ with the ground. The height of the kite above the ground is :

• A. $20\sqrt{3}$ m
• B. 40 m
• C. $40\sqrt{3}$ m
• D. $80\sqrt{3}$ m

Hint:

In a $30^\circ - 60^\circ - 90^\circ$ right triangle:
The side opposite to the $30^\circ$ angle is always exactly half the length of the hypotenuse!
Since the hypotenuse is 80 m, the height must be $80 / 2 = 40 \text{ m}$. This can be answered in seconds without written calculations!

Answer 1

The Correct Option is B

Step 1: Spot the special triangle.
The string, the ground, and the vertical height form a right triangle with the angle of elevation $30^\circ$ and hypotenuse (the string) $=80$ m, that is, a 30-60-90 triangle.
Step 2: Use the standard 30-60-90 side ratio.
In any 30-60-90 right triangle, the side opposite the $30^\circ$ angle is always exactly half the hypotenuse.
Step 3: Apply it here.
Height $=\frac{80}{2}=40$ m.
\[ \boxed{40 \text{ m}} \]