Page 696 - Basic College Mathematics with Early Integers

S E C T I O N 9.6 I CONGRUENT AND SIMILAR TRIANGLES 673

Concept Check The following two triangles are similar.Which vertices of
the first triangle appear to correspond to which vertices of the second triangle?

A
N
M
B
C
O
Many applications involve diagrams containing similar triangles. Surveyors,
astronomers, and many other professionals continually use similar triangles in their
work.

Example 4 Finding the Height of a Tree PRACTICE 4
Tammy Shultz, a firefighter,
Mel Rose is a 6-foot-tall park ranger who needs to know the height of a particular needs to estimate the height of
tree. He measures the shadow of the tree to be 69 feet long when his own shadow a burning building. She esti-
is 9 feet long. Find the height of the tree.
mates the length of her shadow
to be 8 feet long and the length
of the building’s shadow to be
60 feet long. Find the approxi-
mate height of the building if
she is 5 feet tall.
n

6 ft

9 ft 69 ft
n
Solution:
1. UNDERSTAND. Read and reread the problem. Notice that the triangle
formed by the Sun’s rays, Mel, and his shadow is similar to the triangle formed 5 ft
by the Sun’s rays, the tree, and its shadow. 60 ft
8 ft
2. TRANSLATE.Write a proportion from the similar triangles formed.
Mel’s height : 6 9 ; length of Mel’s shadow
height of tree : n = 69 ; length of tree’s shadow
6 3 9
or = Simplify . (ratio in lowest terms)
n 23 69
3. SOLVE for n:

6 3

n 23
# #
6 23 = n 3 Set cross products equal.
#
138 = n 3 Multiply.
138
= n Divide 138 by 3, the number multiplied by n.
3
46 = n
Answer
4. INTERPRET. Check to see that replacing n with 46 in the proportion makes
the proportion true. State your conclusion:The height of the tree is 46 feet. 4. approximately 37.5 ft

Concept Check Answer
Work Practice 4
A corresponds to O; B corresponds
to N; C corresponds to M