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 \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle, the side opposite the \(30^{\circ}\) angle is always half the hypotenuse. Since the string (hypotenuse) is 80 m, the height is simply 40 m.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a right-angled triangle problem where the string is the hypotenuse, and the height of the kite is the perpendicular side relative to the angle with the ground.
Step 2: Key Formula or Approach:
\[ \sin \theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}} \]
Step 3: Detailed Explanation:
Let \(h\) be the height of the kite and \(L = 80\) m be the length of the string.
The angle \(\theta = 30^{\circ}\).
\[ \sin 30^{\circ} = \frac{h}{80} \]
We know that \(\sin 30^{\circ} = \frac{1}{2}\).
\[ \frac{1}{2} = \frac{h}{80} \]
\[ h = \frac{80}{2} = 40 \text{ m} \]
Step 4: Final Answer:
The height of the kite above the ground is 40 m.