Question

example 2: handball demarco is teaching taye how to play handball. taye prefers to return the ball on a serve when it bounces to a height of 42 inches. when demarco serves the ball, where should he aim for the ball to hit the front wall to ensure that it bounces at the short line and up to taye standing 11 feet behind the short line? assume that the angles formed by the path of the bouncing handball are congruent. the front wall forms a ______ angle with the ground, and the height to which the ball bounces forms a 90° angle with the ground. therefore, the two triangles are similar by the ______ postulate.

Explanation:

Step1: Convert units to feet

42 inches = $\frac{42}{12} = 3.5$ feet

Step2: Define variables for unknown height

Let $x$ = height on front wall to aim for.

Step3: Set up proportion (similar triangles)

Triangles are similar by AA Postulate (right angles + congruent bounce angles).
$\frac{x}{25+11} = \frac{3.5}{11}$

Step4: Solve for $x$

$x = \frac{3.5 \times 36}{11}$
$x = \frac{126}{11} \approx 11.45$ feet

Answer:

The front wall forms a $\boldsymbol{90^\circ}$ angle with the ground, and the height to which the ball bounces forms a $90^\circ$ angle with the ground. Therefore, the two triangles are similar by the AA (Angle-Angle) Postulate.
Demarco should aim for a height of $\frac{126}{11}$ feet (or approximately 11.5 feet) on the front wall.