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

The distance $x$ in the figure is required.

The required distance $x=10.67\ \text{ft}$

The given triangles $ABC$ and $CDE$ are similar by Angle Angle.

$\angle B=\angle D=90^{\circ}$

$\angle ACB=\angle ECD$

The ratio of the sides is

$\dfrac{BC}{CD}=\dfrac{12}{9}=\dfrac{4}{3}$

So,

$\dfrac{AB}{ED}=\dfrac{4}{3}\\\Rightarrow \dfrac{x}{8}=\dfrac{4}{3}\\\Rightarrow x=\dfrac{4}{3}\times 8\\\Rightarrow x=10.67\ \text{ft}$

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