A kite is flying at the end of a straight string that has a length of 250 meters. The string makes an angle of 65 degrees with the ground. How high above the ground is the kite?

To find the height of the kite above the ground, we can use basic trigonometry. Specifically, we'll use the sine function since we are dealing with a right triangle, where:

- The length of the string (250 meters) is the hypotenuse.
- The angle between the string and the ground is 65°.
- The height of the kite (which we are trying to find) is the opposite side of the angle.

The sine function is defined as:

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

Substituting in the known values:

\[
\sin(65^\circ) = \frac{h}{250}
\]

Now, solve for \( h \):

\[
h = 250 \times \sin(65^\circ)
\]

Using a calculator:

\[
h \approx 250 \times 0.9063 \approx 226.58 \, \text{meters}
\]

So, the kite is approximately **226.6 meters** above the ground.

Would you like further details or have any other questions? Here are 5 related questions:

1. How would the height change if the string were longer or shorter?
2. How does the angle affect the height of the kite for the same string length?
3. Can we calculate the horizontal distance between the kite and the person holding the string?
4. What if the string was curved due to wind, how could that affect calculations?
5. How would you find the height if the angle given was in radians?

**Tip**: For problems involving angles and lengths, always consider which trigonometric function relates the sides of the triangle best (sine, cosine, or tangent).

Learn how to find the height of a kite flying at the end of a 250-meter string with a 65° angle to the ground. This trigonometry problem demonstrates the use of the sine function to solve for the height of a right triangle. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation