• indirect measurement

• Solve problems involving similar triangles.

8.3 The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. (B) Estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. 8.9 The student uses indirect measurement to solve problems. (B) Use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.

Use Shadow Reckoning

TREES A tree in front of Marcel’s house has a shadow 12 feet long. Marcel’s shadow is 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree?

Use Shadow Reckoning

Answer: The tree is 22 feet tall.

tree’s shadow tree’s heightMarcel’s shadow Marcel’s height

12 ● 5.5 = 3 ● h Find the cross products.

Multiply.

Simplify.

Divide each side by 3.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 4.5 feet

B. 5 feet

C. 5.5 feet

D. 6 feet

Jayson casts a shadow that is 10 feet long. At the same time, a flagpole casts a shadow that is 40 feet long. If the flagpole is 20 feet tall, how tall is Jayson?

Use Indirect Measurement

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

Use Indirect Measurement

Answer: The distance across the stream is 16 meters.

Write a proportion.

AB = 48, ED = d, BC = 60, and DC = 20

Multiply. Then divide each side by 60.

48 ● 20 = d ● 60 Find the cross products.

Simplify.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 6 feet

B. 6.5 feet

C. 7 feet

D. 7.5 feet

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.