Question

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.
14.2 feet
17.1 feet
47.6 feet
55.2 feet

Explanation:

Step1: Calculate height at 25°

$h_1 = 50 \cdot \sin(25^\circ) \approx 50 \cdot 0.4226 = 21.13$

Step2: Calculate height at 45°

$h_2 = 50 \cdot \sin(45^\circ) \approx 50 \cdot 0.7071 = 35.355$

Step3: Find height difference

$\Delta h = h_2 - h_1 \approx 35.355 - 21.13 = 14.2$

Answer:

A. 14.2 feet