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This problem involves a kite, string length, and an angle of elevation. We can solve it using basic trigonometry.

Here’s a breakdown:

1. **Given Information**:
   - The distance from Kaj’s hands to the ground is 3.5 feet.
   - The string length (the hypotenuse of a right triangle) is 75 feet.
   - The angle of elevation from her hand to the kite is \(33^\circ\).

2. **Goal**:
   - We need to find the total height of the kite above the ground.

### Approach:
To find the vertical distance from her hands to the kite (which is the opposite side of the right triangle), we can use the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Substituting the known values:
\[
\sin(33^\circ) = \frac{\text{opposite}}{75}
\]
Solving for the opposite side (which is the height of the kite above her hands):
\[
\text{opposite} = 75 \times \sin(33^\circ)
\]

Finally, we’ll add 3.5 feet (her hand's height) to the result to get the total height of the kite above the ground.

Let me calculate this.The total height of the kite above the ground is approximately **44.35 feet**.

Would you like more details on this or have any questions?

Here are 5 related questions for further exploration:
1. What would the height be if the angle of elevation were \(40^\circ\)?
2. How would the height change if the string length increased to 100 feet?
3. How could you use the cosine function to determine the horizontal distance to the kite?
4. What if Kaj's hands were 4 feet above the ground—how would that change the height?
5. How would the problem change if the string were not fully extended?

**Tip:** In trigonometry problems, always ensure your angle is measured from the correct reference point (e.g., the ground or a horizontal line).

Kaj is flying a kite, holding her hands a distance of 3.5 feet above the ground and letting all the kite’s string play out. She measures the angle of elevation from her hand to the kite to be 33°. If the string from the kite to her hand is 75 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.

Learn how to calculate the height of a kite above the ground when given a string length of 75 feet and an angle of elevation of 33°. This problem involves applying trigonometric functions, such as sine, to a right triangle scenario. Suitable for students in Grades 9-10.

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