Exercise 7 Page 557

We are given the following situation and we want to find the height of the nearby man.

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.

If we 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 Angle-Angle (AA) Similarity rule. This means that the ratio of the heights of the Giant Wheel and the man will be equal to the ratio of the lengths of their shadows. Height of the Giant Wheel/Height of the Man = Shadow of the Giant Wheel/Shadow of the Man ⇓ 136/h=34/1 12 Let's solve this proportion using cross products.

136/h=34/1 12

CrossMult

Cross multiply

136 * 1 12 = 34 * h

MixedToFrac

a bc=a* c+b/c

136 * 3/2 = 34 * h

▼

Solve for h

MoveLeftFacToNum

a*b/c= a* b/c

136 * 3/2 = 34 * h

Multiply

Multiply

408/2 = 34 h

CalcQuot

Calculate quotient

204 = 34 h

DivEqn

.LHS /34.=.RHS /34.

204/34=34 h/34

CalcQuot

Calculate quotient

6=h

RearrangeEqn

Rearrange equation

h=6

The man is 6 feet tall.