Exercise 22 Page 566

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

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. h/5=10 12/3 Now, we will solve the above equation using cross multiplication.

h/5=10 12/3

CrossMult

Cross multiply

h* 3=5* 10 12

▼

Solve for h

WriteDec

Write as a decimal

h*3=5*10.5

Multiply

Multiply

3h=52.5

DivEqn

.LHS /3.=.RHS /3.

h=52.5/3

CalcQuot

Calculate quotient

h=17.5

The height of the statue is 17.5 feet.