Exercise 3 Page 557

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

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 building and house will be equal to the ratio of the lengths of their shadows. Height of the Building/Height of the House=Shadow of the Building/Shadow of the House ⇓ h/50=50/12.5 Now, we will solve this proportion using cross products.

h/50=50/12.5

CrossMult

Cross multiply

h* 12.5=50* 50

▼

Solve for h

Multiply

Multiply

h* 12.5=2500

DivEqn

.LHS /12.5.=.RHS /12.5.

h* 12.5/12.5=2500/12.5

MoveLeftFacToNum

a*b/c= a* b/c

h * 12.5/12.5=2500/12.5

QuotOne

a/a=1

h * 1=2500/12.5

IdPropMult

Identity Property of Multiplication

h =2500/12.5

CalcQuot

Calculate quotient

h=200

The height of the building is 200 feet.