Question

A hockey player passes a puck to his teammate by bouncing it off a wall. The angles formed when the puck hits the wall and bounces off are congruent. Some of the distances are shown.
What is the distance, x, from Player 1 to the wall?

Enter your answer, as a decimal, in the box. Round your answer to the nearest hundredth.

Answer 1

X     8-- = --12    9
96 = 9x
x = 10.67 ft.

Answer 2

Two different triangles for player 1 and player 2

Both triangles have right angle and same angle where they are connected. So other angle is also same.

All angles are same so they are similar triangles.

smaller triangle is similar to larger triangle

Hence the sides are in proportion

$\frac{x}{8} = \frac{12}{9}$

So x * 9 = 12 * 8

9x = 96

Divide by 9 on both sides

x = 10.67 ft