Every bounce, the ball bounces to 75% of its previous bounce, so the first few bounces will give us heights of
20 ft (0 bounces)
20 × 0.75 = 15 ft (1 bounce)
20 × 0.75 × 0.75 = 11.25 ft (2 bounces)
We can express the continued multiplication by 0.75 as an exponent, so that after the nth bounce, the ball will bounce feet. Plugging in 18 for n gets us
X - difference between the height of the basketball hoop and the vertical distance from the ground to Clair´s eyes. Using T O A: tan (9.2°) = x / 22 ft x = tan (9.2°) · 22 ft x = 0.162 · 22 ft x = 3.564 ft The height of the basketball hoop is: h = 5.6 + 3.564 = 9.164 feet
