1. 5-7 Indirect Measurement Warm Up Problem of the Day
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up Solve each proportion. = = 1. 2. = = 3. 4. x 75 3 5 2.4 8 6 x
9 27 = 8 7 x
3.5 = 3. 4.
x = 4
x = 2

3. Problem of the Day
A plane figure is dilated and gets 50% larger. What scale factor should you use to dilate the figure back to its original size? (Hint: The answer is not .)
1 2
2 3

4. Learn to find measures indirectly by applying the properties of similar figures.

5. Vocabulary
indirect measurement

6. Sometimes, distances cannot be measured directly
Sometimes, distances cannot be measured directly. One way to find such a distance is to use indirect measurement, a way of using similar figures and proportions to find a measure.

7. Additional Example 1: Geography Application
Triangles ABC and EFG are similar. Find the length of side EG. F E G
9 ft x B A C
3 ft
4 ft
Triangles ABC and EFG are similar.

8. Additional Example 1 Continued
Triangles ABC and EFG are similar. Find the length of side EG. AB AC EF EG =
Set up a proportion.
Substitute 3 for AB, 4 for AC, and 9 for EF. 3 4 9 x =
3x = 36
Find the cross products. 3x 3 36 3 =
Divide both sides by 3.
x = 12
The length of side EG is 12 ft.

9. Triangles DEF and GHI are similar. Find the length of side HI.
Check It Out: Example 1
Triangles DEF and GHI are similar. Find the length of side HI. H G I
8 in x E D F
7 in
2 in
Triangles DEF and GHI are similar.

10. Check It Out: Example 1 Continued
Triangles DEF and GHI are similar. Find the length of side HI. DE EF GH HI =
Set up a proportion.
Substitute 2 for DE, 7 for EF, and 8 for GH. 2 7 8 x =
2x = 56
Find the cross products. 2x 2 56 2 =
Divide both sides by 2.
x = 28
The length of side HI is 28 in.

11. Understand the Problem
Additional Example 2: Problem Solving Application
A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree? 1
Understand the Problem
The answer is the height of the tree.
List the important information:
• The length of the building’s shadow is 75 ft.
• The height of the building is 30 ft.
• The length of the tree’s shadow is 35 ft.

12. Additional Example 2 Continued
Make a Plan
Use the information to draw a diagram.
35 feet
75 feet
30 feet h
Solve 3
Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

13. Additional Example 2 Continued
Solve 3 30 75 h 35
Corresponding sides of similar figures are proportional. =
75h = 1050
Find the cross products.
75h 75
1050 75 =
Divide both sides by 75.
h = 14
The height of the tree is 14 feet.

14. Additional Example 2 Continued4
Look Back 75 30
Since = 2.5, the building’s shadow is
2.5 times its height. So, the tree’s shadow should also be 2.5 times its height and 2.5 of 14 is 35 feet.

15. Understand the Problem
Check It Out: Example 2
A 24-ft building casts a shadow that is 8 ft long. A nearby tree casts a shadow that is 3 ft long. How tall is the tree? 1
Understand the Problem
The answer is the height of the tree.
List the important information:
• The length of the building’s shadow is 8 ft.
• The height of the building is 24 ft.
• The length of the tree’s shadow is 3 ft.

16. Check It Out: Example 2 Continued
Make a Plan
Use the information to draw a diagram.
3 feet
8 feet
24 feet h
Solve 3
Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

17. Check It Out: Example 2 Continued
Solve 3 24 8 h 3
Corresponding sides of similar figures are proportional. =
72 = 8h
Find the cross products. 72 8 8h 8 =
Divide both sides by 8.
9 = h
The height of the tree is 9 feet.

18. Check It Out: Example 2 Continued4
Look Back 8 24 1 3
Since = , the building’s shadow is
times its height. So, the tree’s
shadow should also be times its
height and of 9 is 3 feet. 1 3 1 3 1 3

19. Lesson Quiz
1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river?
2. A yardstick casts a 2-ft shadow. At the same time, a tree casts a shadow that is 6 ft long. How tall is the tree?
7.98 m w
7 m
5 m
5.7 m
9 ft