Exercise 12 Page 558

We are given the following picture and we want to find the height of the statue.

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

Let's think about the ground as a transversal and the sunbeams as parallel lines. The angles created between them 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 statue and Mila will be equal to the ratio of the lengths of their shadows. Height of the Statue/Height of the Girl=Shadow of the Statue/Shadow of the Girl ⇓ x/4 12=12/6 We can solve this proportion using cross products.

x/4 12=12/6

CrossMult

Cross multiply

x* 6 = 12 * 4 12

▼

Solve for x

Rewrite

Rewrite 4 12 as 4.5

x* 6 = 12 * 4.5

Multiply

Multiply

6x =54

DivEqn

.LHS /6.=.RHS /6.

6x/6=54/6

CalcQuot

Calculate quotient

x=9

The height of the statue is 9 feet. This corresponds to answer B.