Question

Find length of a kite string flying at 100 m above the ground with the elevation 60°.

• A. \(\frac {100}{\sqrt 3}\)
• B. \(\frac {50}{\sqrt 3}\)
• C. \(\frac {200}{\sqrt 3}\)
• D. \(\frac {25}{\sqrt 3}\)

Answer 1

The Correct Option is C

To solve the problem, we need to find the length of the kite string when the kite is flying at a height of 100 meters and the angle of elevation is $60^\circ$.

1. Understanding the Triangle Formed:
The kite string, the vertical height (100 m), and the ground form a right-angled triangle where:
- Opposite side = 100 m (height)
- Hypotenuse = length of the kite string (we need to find this)
- Angle of elevation = $60^\circ$

2. Using Trigonometry (Sine Function):
$ \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} $
So, $ \sin 60^\circ = \frac{100}{\text{Length of string}} $

3. Solving for Length of String:
$ \sin 60^\circ = \frac{\sqrt{3}}{2} $
Therefore, $ \frac{\sqrt{3}}{2} = \frac{100}{\text{Length}} $

$ \text{Length} = \frac{100 \times 2}{\sqrt{3}} = \frac{200}{\sqrt{3}} $

Final Answer:
The length of the kite string is $ \mathbf{\frac{200}{\sqrt{3}}} $.