Exercise 29 Page 567

Let's begin with recalling that, according to the Angle-Angle Similarity Theorem, if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the drawn triangles are similar.

We are given that the ball landed 23 of the way between Luis's dad and and Luis. If we call d the distance between them, then we can write the length of corresponding sides. Let x be the height at which Luis caught the ball.

To find the value of x, we will create a proportion using the fact that in similar triangles the corresponding sides are proportional. 40/x=23d/13d Let's solve the above equation. We will start with reducing the fraction on the right-hand side by d.

40/x=23d/13d

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Simplify right-hand side

ReduceFrac

a/b=.a /d./.b /d.

40/x=23/13

DivFracByFracD

.a /b./.c /d.=a/b*d/c

40/x=2/3*3/1

MultFrac

Multiply fractions

40/x=6/3

ReduceFrac

a/b=.a /3./.b /3.

40/x=2/1

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Solve for x

CrossMult

Cross multiply

40*1=x*2

Multiply

Multiply

40=2x

DivEqn

.LHS /2.=.RHS /2.

20=x

RearrangeEqn

Rearrange equation

x=20

Luis caught the ball at the height of 20 inches.