To solve this problem, we need to use trigonometry. We are given the following:

• The height of Savannah's hand from the ground is 2.5 feet.
• The length of the string is 75 feet.
• The angle of elevation is 32°.

We are tasked with finding how high the kite is above the ground.

Approach:

We can use the sine function from trigonometry:

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

Where:

• $\theta = 32^\circ$
• Opposite is the vertical distance from Savannah's hand to the kite.
• Hypotenuse is the length of the string, which is 75 feet.

Steps:

1. The opposite side (height from her hand to the kite) can be calculated using:

$\sin(32^\circ) = \frac{h}{75}$

2. Solve for $h$:

$h = 75 \times \sin(32^\circ)$

3. Add the height of Savannah's hand (2.5 feet) to the height of the kite above her hand to get the total height of the kite from the ground.

Let me compute this for you! math

Given values

angle = 32 # degrees hypotenuse = 75 # feet hand_height = 2.5 # feet

Convert angle to radians

angle_radians = math.radians(angle)

Calculate the height of the kite from her hand

height_above_hand = hypotenuse * math.sin(angle_radians)

Total height of the kite from the ground

total_height = height_above_hand + hand_height

Round the result to the nearest tenth

total_height_rounded = round(total_height, 1) total_height_roundedThe kite is approximately 42.2 feet above the ground.

Would you like further details on how I solved this, or do you have any other questions? Here are a few related topics you might find helpful:

1. How do different trigonometric functions (cosine, tangent) relate to real-world problems?
2. How can we calculate the height of objects when the angle of elevation is measured from different points?
3. What are the differences between using sine, cosine, and tangent in right triangles?
4. How does the length of the hypotenuse affect the height calculation in this context?
5. What is the relationship between angle of elevation and the height of an object?

Tip: When solving trigonometric problems, always ensure your calculator is in the correct mode (degrees or radians) based on the angle's units!