Suppose you are flying a kite that is 50 feet long. While flying, there is a constant gust of wind that blows the kite to an angle of 60° with the ground. How high, in feet, is the kite above the ground?

This problem can be solved using trigonometry, specifically by using the sine function, which relates the angle of a right triangle to the ratio of the opposite side (the height in this case) to the hypotenuse (the length of the kite string).

The formula for sine is:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Where:
- \(\theta = 60^\circ\) (the angle between the kite string and the ground),
- The hypotenuse is the length of the kite string, which is 50 feet,
- The opposite side is the height of the kite above the ground.

We can rearrange the formula to solve for the height (opposite side):

\[
\text{height} = \sin(60^\circ) \times \text{length of the string}
\]

\[
\text{height} = \sin(60^\circ) \times 50
\]

Since \(\sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866\):

\[
\text{height} = 0.866 \times 50 = 43.3 \text{ feet}
\]

Therefore, the kite is approximately **43.3 feet** above the ground.

Would you like more details on any step or have any questions?

### Related Questions:
1. How would the height change if the angle were 45° instead of 60°?
2. What would happen if the kite string were 100 feet long?
3. How could we calculate the horizontal distance between you and the kite?
4. How does the sine function apply to real-world problems like this one?
5. What trigonometric function would be used to find the horizontal distance?

### Tip:
The sine function is useful for finding the height of an object when you know the angle and the length of the hypotenuse in a right triangle!

Learn how to calculate the height of a kite above the ground using the sine function and a right triangle. This problem involves flying a 50-foot-long kite at an angle of 60° with the ground, perfect for students in Grades 9-12 studying trigonometry.

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