Questions: Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25° angle with the ground and when the string makes a 45° angle with the ground? Round to the nearest tenth.

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25° angle with the ground and when the string makes a 45° angle with the ground? Round to the nearest tenth.

Transcript text: Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a $25^{\circ}$ angle with the ground and when the string makes a $45^{\circ}$ angle with the ground? Round to the nearest tenth.

Solution

Solution Steps

Step 1: Determine the Height of the Kite at a $25^{\circ}$ Angle

To find the height of the kite when the string makes a $25^{\circ}$ angle with the ground, we use the sine function. The height $h_1$ can be calculated as follows:

\[ h_1 = 50 \times \sin(25^{\circ}) \]

Using a calculator, we find:

\[ h_1 \approx 50 \times 0.4226 = 21.13 \text{ feet} \]

Step 2: Determine the Height of the Kite at a $45^{\circ}$ Angle

Similarly, to find the height of the kite when the string makes a $45^{\circ}$ angle with the ground, we use the sine function. The height $h_2$ is:

\[ h_2 = 50 \times \sin(45^{\circ}) \]

Using a calculator, we find:

\[ h_2 \approx 50 \times 0.7071 = 35.36 \text{ feet} \]

Step 3: Calculate the Difference in Heights

The difference in the height of the kite between the two angles is:

\[ \Delta h = h_2 - h_1 = 35.36 - 21.13 = 14.23 \text{ feet} \]

Rounding to the nearest tenth, we get: