Exercise 19 Page 560

We are told that Horatio is 6 feet tall and casts a shadow that is 3 feet long. We are also told that the tower casts a shadow that is 25 feet long. We want to find the height of the tower.

We can see that this is a shadow problem. We can assume that the angles formed by the sunbeams when the objects are hit by the light are congruent. The two shapes that are created by the sunbeams are right triangles.

We can think about the ground as a transversal and the sunbeams as parallel lines. Then the angles created are corresponding angles. Since two pairs of corresponding angles are congruent, the above triangles are similar by the rule for Angle-Angle (AA) Similarity. This means that the ratio of the heights of the tower and Horatio will be equal to the ratio of the lengths of their shadows. Height of the Tower/Height of Horatio=Shadow of the Tower/Shadow of Horatio ⇓ h/6=25/3 Now, we will solve this proportion using cross products.

h/6=25/3

CrossMult

Cross multiply

h* 3=25* 6

▼

Solve for h

Multiply

Multiply

h* 3=150

DivEqn

.LHS /3.=.RHS /3.

h* 3/3=150/3

MoveLeftFacToNum

a*b/c= a* b/c

h * 3/3=150/3

QuotOne

a/a=1

h * 1=150/3

IdPropMult

Identity Property of Multiplication

h =150/3

CalcQuot

Calculate quotient

h=50

The height of the tower is 50 feet. This means that the correct option is B.