Chapter 7.3, Problem 29PPS

To determine

To find: the height did the Luis catch the ball.

Answer to Problem 29PPS

  $20\text{ inch}$ .

Explanation of Solution

Given:

A ball is thrown by the Luis and the ball is two-third of the way between them before it bounced back.

When the ball is thrown, the angle formed by the path is concurrent.

  

Calculation:

From the given figure,

  $\begin{array}{l}\angle D=\angle E\{\text{given}}\\ \angle ABD=\angle CBE\{\text{given}}\\ \therefore \Delta ABD\sim \Delta CBE\{\text{by AA-similarity}}\end{array}$ .

Therefore, the corresponding parts of similar triangle is proportion.

  $\begin{array}{l}\frac{AB}{BC}=\frac{AD}{CE}\\ \Rightarrow \frac{40}{\frac{2}{3}x}=\frac{h}{\frac{1}{3}x}\{\text{substitutes these value}}\\ \Rightarrow h=\frac{40\times \frac{1}{3}x}{\frac{2}{3}x}\{\text{simplify} }\\ \Rightarrow h=\frac{40}{2}=20\end{array}$

Hence, the height did the Luis catch the ball is $20\text{ inch}$ .