Answer:
The distance X from the floor that the boy caught the ball is 26.67 in.
Step-by-step explanation:
Given :
A man throws around a basketball from 30 inches above the ground.
The basketball bounces off the floor and a boy catches it the distance the ball traveled from the man to the floor is 45 inches .
The distance the ball traveled from the floor to the boy is 40 inches
The angles formed by the basketballs path are congruent .
To Find : Value of x
Solution :
Since the angles formed by the basketball path are congruent so we can use trigonometric ratios.
Since angles formed by basketball path are equal i.e. ∠A = ∠D (Refer the attached file)
⇒\(Sin A = Sin D\)
⇒\(Sin A= \frac{perpendicular }{hypotenuse} = \frac{AB}{AC} =\frac{30}{45}\)
⇒\(Sin D = \frac{perpendicular }{hypotenuse} = \frac{EF}{ED} =\frac{x}{40}\)
Since Sin A = Sin D
⇒\(\frac{30}{45} =\frac{x}{40}\)
⇒\(\frac{30*40}{45} =x\)
⇒\(\frac{1200}{45} =x\)
⇒\(26.67 =x\)
Thus , The distance X from the floor that the boy caught the ball is 26.67 in.
