Brian’s kite is flying above a field at the end of 65 m of string. If the angle of elevation to the kite
measures 70°, how high is the kite above Brian’s head?

To find the height of the kite above Brian's head, we can model the situation as a right triangle. The length of the string (65 m) represents the hypotenuse, and the height of the kite is the opposite side of the right triangle, which we are trying to find. The angle of elevation is 70°.

Using trigonometry, specifically the sine function, we can write the equation:

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

Substitute the known values:

\[
\sin(70^\circ) = \frac{h}{65}
\]

Solve for \(h\) (the height of the kite):

\[
h = 65 \times \sin(70^\circ)
\]

Now we can calculate the value.

\[
h = 65 \times 0.9397 \approx 61.08 \, \text{m}
\]

Thus, the kite is approximately **61.08 meters** above Brian's head.

Would you like more details or have any questions? Here are some related questions to consider:

1. What is the length of the string if the kite is at a different angle of elevation?
2. How would the problem change if the string was longer or shorter?
3. What if the wind caused the kite to be lower? How would the height change?
4. Can you calculate the horizontal distance from Brian to the point directly under the kite?
5. How would you find the height if you were given the horizontal distance instead?

**Tip:** Always remember to check whether you're dealing with right triangles when applying basic trigonometry.

Brian’s kite is flying above a field at the end of 65 m of string. If the angle of elevation to the kite measures 70°, how high is the kite above Brian’s head?

Learn how to calculate the height of a kite flying above a field using trigonometry. Given a 65-meter string and an angle of elevation of 70°, we use the sine function to find that the kite is approximately 61.08 meters above Brian's head. Suitable for students in Grades 9-10.

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