Taylor lets out 120 meters of kite string, then wonders how high the kite has risen.

Taylor is able to calculate the answer, after using a protractor to measure the 63-degree angle of

elevation that the string makes with the ground. How high is the kite, to the nearest meter? What

(unrealistic) assumptions did you make in answering this question?

We can solve this problem using basic trigonometry. Since the kite string forms an angle of elevation with the ground, we can imagine a right triangle where:

- The hypotenuse is the length of the kite string (120 meters).
- The angle of elevation is 63 degrees.
- The height of the kite is the opposite side to the angle of elevation.

The relationship between the opposite side (height) and the hypotenuse in a right triangle is given by the sine function:

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

Where:
- \(\theta = 63^\circ\) (angle of elevation),
- Hypotenuse = 120 meters (length of the kite string),
- Opposite (height of the kite) = ?

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

\[
\text{height} = \text{hypotenuse} \times \sin(\theta)
\]

Substituting the values:

\[
\text{height} = 120 \times \sin(63^\circ)
\]

Now let's calculate that.

\[
\sin(63^\circ) \approx 0.8910
\]

\[
\text{height} \approx 120 \times 0.8910 = 106.92 \text{ meters}
\]

To the nearest meter, the kite is about **107 meters high**.

### Assumptions:
1. The string is perfectly straight and taut, with no sagging.
2. The kite is directly above the point on the ground where Taylor is standing (ignoring wind or horizontal movement).
3. There is no air resistance or wind affecting the shape of the string.
4. The ground is flat and level.
  
Would you like more details on the assumptions or steps?

### Related Questions:
1. How would wind affect the height calculation?
2. What if the string was not taut? How would the calculation change?
3. How could Taylor account for the sag in the string?
4. What trigonometric function would apply if the angle of elevation was larger?
5. How would the problem change if the kite was moving horizontally?

### Tip:
For real-world problems, always consider external factors like tension, wind, and string weight when applying idealized models.

Taylor lets out 120 meters of kite string, then wonders how high the kite has risen. Taylor is able to calculate the answer after using a protractor to measure the 63-degree angle of elevation that the string makes with the ground. How high is the kite, to the nearest meter? What (unrealistic) assumptions did you make in answering this question?

Learn how to calculate the height of a kite using basic trigonometry. Given 120 meters of kite string and a 63-degree angle of elevation, this step-by-step solution demonstrates the use of sine function in a right triangle. The final height is approximately 107 meters. Suitable for students in Grades 9-10.

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