Pre-Algebra Chapter 9
Pre-Algebra Chapter 9
Pre-Algebra Chapter 9
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The properties of similar triangles can be used to determine missing<br />
measures in shadow problems. This is called shadow reckoning.<br />
Example 3<br />
Use Shadow Reckoning<br />
LANDMARKS Suppose the Space<br />
Needle in Seattle, Washington, casts<br />
a 220-foot shadow at the same time a<br />
nearby tourist casts a 2-foot shadow.<br />
If the tourist is 5.5 feet tall, how tall<br />
is the Space Needle?<br />
Explore<br />
Plan<br />
Solve<br />
Examine<br />
You know the lengths of the<br />
shadows and the height of the<br />
tourist. You need to find the<br />
Space Needle’s height.<br />
Write and solve a proportion.<br />
tourist’s height →<br />
Space Needle’s height →<br />
5 .5 2 2<br />
h 20 <br />
5.5 ft<br />
5.5 220 h 2 Find the cross products.<br />
1210 2h Multiply.<br />
605 h Mentally divide each side by 2.<br />
The height of the Space Needle is 605 feet.<br />
The tourist’s height is a little less than 3 times the length of his or<br />
her shadow. The space needle should be a little less than 3 times<br />
its shadow, or 3 220, which is 660 feet. So, 605 is reasonable.<br />
2 ft<br />
h ft<br />
220 ft<br />
Not drawn to scale<br />
← tourist’s shadow<br />
← Space Needle’s shadow<br />
Concept Check<br />
Guided Practice<br />
GUIDED PRACTICE KEY<br />
1. OPEN ENDED Draw two similar triangles and label the vertices. Then<br />
write a proportion that compares the corresponding sides.<br />
2. Explain indirect measurement in your own words.<br />
In Exercises 3 and 4, the triangles are similar. Write a proportion to find each<br />
missing measure. Then find the value of x.<br />
3. R<br />
4.<br />
C<br />
9 ft<br />
6 ft<br />
S<br />
x ft<br />
T<br />
6 cm<br />
A<br />
P<br />
6 cm<br />
N<br />
2 cm<br />
M<br />
D<br />
15 ft<br />
E<br />
B<br />
x cm<br />
C<br />
Applications<br />
5. MAPS In the figure,<br />
ABC EDC. Find<br />
the distance from<br />
Austintown to North<br />
Jackson.<br />
Deerfield<br />
A<br />
North Jackson<br />
D<br />
2 km<br />
18 km<br />
Austintown<br />
x km E<br />
C<br />
6 km<br />
Ellsworth<br />
B<br />
www.pre-alg.com/extra_examples<br />
6. SHADOWS At the same time a 10-foot flagpole casts an 8-foot shadow, a<br />
nearby tree casts a 40-foot shadow. How tall is the tree?<br />
Lesson 9-7 Similar Triangles and Indirect Measurement 473
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