Basic Mathematics for College Students

760 Chapter 9 An Introduction to Geometry

The lengths of corresponding sides of these similar triangles are proportional.

Find each cross product and set them equal.

Do the multiplication.

To isolate x, undo the multiplication by 32 by

dividing both sides by 32.

Thus, is 30.

b.To find , we write a proportion of corresponding side lengths in such a way

that is the only unknown.

Find each cross product and set them equal.

Do the multiplication.

To isolate y, undo the multiplication by 48 by

dividing both sides by 48.

Thus, is 24.y

y 24

48 y1,152

48 y32(36)

Substitute: RT48, JL32, RS36,

(^) and JKy.

48

32



36

y

RT

JL



RS

JK

y

y

x

30 x

960  32 x

48(20) 32 x

Substitute: RT 48, JL32, STx, and

(^) KL20.

48

32



x

20

Each fraction is a ratio of a side length of RST

(^) to its corresponding side length of JKL.

RT

JL



ST

KL

4 Use similar triangles to find unknown

lengths in application problems.

Similar triangles and proportions can be used to find lengths that would normally be

difficult to measure. For example, we can use the reflective properties of a mirror to

calculate the height of a flagpole while standing safely on the ground.

30

32  960

 96

00

 00

0

48

 20

960

24

48 1,152

 96

192

 192

0

36

 32

72

1080

1152

EXAMPLE (^7) To determine the height of a flagpole, a woman walks to a
point 20 feet from its base, as shown below. Then she takes a mirror from her purse,
places it on the ground, and walks 2 feet farther away, where she can see the top of
the pole reflected in the mirror. Find the height of the pole.
B h
C E
A
D
2 ft 20 ft
5 ft
The woman’s eye level
is 5 feet from the ground.
StrategyWe will show that.
WHYThen we can write a proportion of corresponding sides so that is the only
unknown and we can solve the proportion for.
SolutionTo show that , we begin by applying an important fact
about mirrors. When a beam of light strikes a mirror, it is reflected at the same angle
as it hits the mirror. Therefore,. Furthermore, because
the woman and the flagpole are perpendicular to the ground. Finally, if two pairs of

BCA  DCE A  E

ABCEDC

h

h

ABCEDC

Self Check 7

In the figure below,

ABCEDC. Find .h

Now TryProblem 85

C D

A

E

h

B

25 ft

40 ft 2 ft