Exercise 8 Page 565

Let's draw a simplified picture that describes the situation. Let h be the height of a cell phone tower.

Since this is an example of a shadow problem, we can assume that the angles formed by the Sun's rays with any two objects are congruent and that the two objects form the sides of two rights triangles.

Since two pairs of angles are congruent, the above triangles are similar by the Angle-Angle Similarity Postulate. This means that the ratio of heights of these objects will be equal to the ratio of their shadow's lengths. Let's rewrite inches as feet using the fact that 1 in. = 112 ft. h/4 612=100/3 412 Now, we will solve the above equation using cross multiplication.

h/4 612=100/3 412

CrossMult

Cross multiply

h* 3 412=4 612* 100

▼

Solve for h

ReduceFrac

a/b=.a /4./.b /4.

h* 3 13=4 612* 100

ReduceFrac

a/b=.a /6./.b /6.

h* 3 13=4 12* 100

MixedToFrac

a bc=a* c+b/c

h*10/3=9/2*100

MoveLeftFacToNum

a*b/c= a* b/c

10h/3=9/2*100

MoveRightFacToNum

a/c* b = a* b/c

10h/3=900/2

CalcQuot

Calculate quotient

10h/3=450

MultEqn

LHS * 3=RHS* 3

10h=450*3

DivEqn

.LHS /10.=.RHS /10.

h=450*3/10

Multiply

Multiply

h=1350/10

CalcQuot

Calculate quotient

h=135

The height of the cell phone tower is 135 feet.