To solve the problem, we can use trigonometry. Here's a step-by-step explanation:

Step 1: Understand the problem

Nasim is holding the kite string at a height of 2.5 feet above the ground. The string forms an angle of elevation of $28^\circ$ from his hand to the kite. The string length (hypotenuse of the triangle) is $105$ feet. We need to calculate how high the kite is above the ground.

Step 2: Use the sine function

In a right triangle: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Here:

• $\theta = 28^\circ$
• Opposite side = vertical distance from the kite to Nasim's hands ($h_{\text{kite}}$)
• Hypotenuse = string length = $105 \, \text{ft}$

$\sin(28^\circ) = \frac{h_{\text{kite}}}{105}$

Solve for $h_{\text{kite}}$: $h_{\text{kite}} = 105 \cdot \sin(28^\circ)$

Step 3: Add the height of Nasim's hands

The total height of the kite above the ground is: $\text{Height of kite above ground} = h_{\text{kite}} + 2.5$

Step 4: Perform the calculations

Let me calculate this: math

Given values

theta_degrees = 28 # Angle of elevation in degrees string_length = 105 # Length of the string in feet hand_height = 2.5 # Height of Nasim's hands above the ground in feet

Convert angle to radians for calculation

theta_radians = math.radians(theta_degrees)

Calculate the vertical height from Nasim's hands to the kite

kite_height_from_hands = string_length * math.sin(theta_radians)

Calculate the total height of the kite above the ground

total_kite_height = kite_height_from_hands + hand_height

kite_height_from_hands, total_kite_height### Calculation Results:

1. The height of the kite from Nasim's hands is approximately 49.29 feet.
2. The total height of the kite above the ground is approximately 51.79 feet.

Would you like a detailed breakdown of any specific step or further clarifications?

Related Questions:

1. What is the formula for calculating distances using trigonometric functions?
2. How would the calculation change if the string length or angle increased?
3. What happens if the height of Nasim’s hands changes?
4. How do you convert between degrees and radians in trigonometry?
5. Can cosine or tangent be used to solve this problem? Why or why not?

Tip:

When solving triangle-based problems, always double-check which trigonometric function (sine, cosine, tangent) applies to avoid errors.