Hugo and Jane were flying a kite. They let out 600 feet of stream if Jane anchored the kite at a 40° angle of inclination what is the height of the kite use units and round to the nearest feet?

To find the height of the kite, we can apply trigonometry, specifically the sine function. We are given:

- The length of the string (hypotenuse) = 600 feet
- The angle of inclination = 40°

We want to find the height (opposite side), which we’ll denote as \( h \). Using the sine function, which is defined as:

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

Substituting the given values:

\[
\sin(40^\circ) = \frac{h}{600}
\]

Solving for \( h \):

\[
h = 600 \times \sin(40^\circ)
\]

Now calculating:

\[
h \approx 600 \times 0.6428 = 385.68 \text{ feet}
\]

Rounding to the nearest foot:

\[
h \approx 386 \text{ feet}
\]

### Final Answer:
The height of the kite is approximately **386 feet**.

Would you like more details or further clarifications? Here are some related questions:

1. How do you calculate the length of the string if you know the height and the angle?
2. What is the cosine of the angle, and how could it help find horizontal distance?
3. How would this problem change if the angle of inclination increased?
4. Can the tangent function also be applied here? If so, how?
5. What other real-life situations use trigonometry in a similar way?

**Tip:** When using trigonometric functions, always ensure your calculator is set to the correct mode (degrees or radians) depending on the problem.

Hugo and Jane were flying a kite. They let out 600 feet of string. If Jane anchored the kite at a 40° angle of inclination, what is the height of the kite? Use units and round to the nearest foot.

Solve a trigonometry problem where Hugo and Jane let out 600 feet of string for their kite at a 40° angle of inclination. Learn how to calculate the height of the kite using the sine function, applicable for students in Grades 9-11. Step-by-step solution included.

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