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The image shows a problem involving a right triangle, where a kite is flying with a string of length 80 meters, and the angle of elevation of the string is 40°. The goal is to find the height \(x\) of the kite above the ground.

We can use trigonometry to solve this. Specifically, we use the sine function, which relates the angle of elevation to the opposite side (the height of the kite, \(x\)) and the hypotenuse (the length of the string, 80 m):

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

In this case:
\[
\sin(40^\circ) = \frac{x}{80}
\]

Now, solving for \(x\):
\[
x = 80 \times \sin(40^\circ)
\]

Using a calculator:
\[
x = 80 \times 0.6428 \approx 51.42
\]

So, the height of the kite is approximately **51 meters** to the nearest meter.

Would you like more details or have any questions?

Here are five related questions to expand on this:

1. How would you calculate the horizontal distance from the person to the kite?
2. How does changing the angle of elevation affect the height of the kite?
3. What if the string were 100 meters long instead? What would the new height be?
4. How can you use cosine to find the horizontal distance in this problem?
5. What assumptions are made in this problem regarding the string?

**Tip:** When solving trigonometric problems, always ensure your calculator is set to the correct mode (degrees or radians) based on the angle provided.

A kite is flying at an angle of elevation of 40°. All 80 m of string have been let out. Ignoring the sag in the string, what is the height of the kite to the nearest meter?

Learn how to calculate the height of a kite using trigonometry with an angle of elevation of 40° and a string length of 80 meters. This problem involves applying the sine function to solve for the height in a right triangle. Suitable for students in Grades 9-10.

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