Let's use trigonometry to find the length of the kite string. In a right-angled triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side.
In this case, the elevation angle is 60 degrees, and the height above the ground is 100 meters. Let \( x \) be the length of the kite string.
\[ \tan(60^\circ) = \frac{\text{height}}{\text{length of the string}} \]
\[ \tan(60^\circ) = \frac{100}{x} \]
\[ \sqrt{3} = \frac{100}{x} \]
Now, solve for \( x \):
\[ x = \frac{100}{\sqrt{3}} = \frac{100 \cdot \sqrt{3}}{3} \]
So, the length of the kite string is \( \frac{100 \cdot \sqrt{3}}{3} \) meters.
The closest option is \( \frac{100 \cdot \sqrt{3}}{3} \), which corresponds to option (d) 100√3 m.
Answers & Comments
Answer:
D) 100√3
Let's use trigonometry to find the length of the kite string. In a right-angled triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side.
In this case, the elevation angle is 60 degrees, and the height above the ground is 100 meters. Let \( x \) be the length of the kite string.
\[ \tan(60^\circ) = \frac{\text{height}}{\text{length of the string}} \]
\[ \tan(60^\circ) = \frac{100}{x} \]
\[ \sqrt{3} = \frac{100}{x} \]
Now, solve for \( x \):
\[ x = \frac{100}{\sqrt{3}} = \frac{100 \cdot \sqrt{3}}{3} \]
So, the length of the kite string is \( \frac{100 \cdot \sqrt{3}}{3} \) meters.
The closest option is \( \frac{100 \cdot \sqrt{3}}{3} \), which corresponds to option (d) 100√3 m.