Lesson Menu Main Idea and New Vocabulary NGSSS Example 1:Use Shadow Reckoning Example 2:Use Indirect Measurement Five-Minute Check.

Main Idea and New Vocabulary

NGSSS

Example 1: Use Shadow Reckoning

Example 2: Use Indirect Measurement

Five-Minute Check

• Solve problems involving similar triangles.

• indirect measurement

MA.8.G.2.1 Use similar triangles to solve problems that include height and distances.

Use Shadow Reckoning

FLAGPOLES A flagpole near a city parking area casts a 22-foot shadow. At the same time, a 3.5-foot-tall parking meter casts a 2-foot shadow. How tall is the flagpole?

Use Shadow Reckoning

Answer: The flagpole is 38.5 feet tall.

Shadow Height

flagpoleparking meter

flagpoleparking meter

22 • 3.5 = 2 • h Find the cross products.

77 = 2h Multiply.

Divide each side by 2.

38.5 = h

A. 6 feet

B. 12 feet

C. 14.8 feet

D. 23.52 feet

SWINGS At the same time a 5-foot tall fence casts a 7-foot shadow, a nearby swingset casts a 16.8 shadow. How tall is the swingset?

LAKES The two triangles shown in the figure are similar. Find the distance across the lake.

Use Indirect Measurement

Write a proportion using the corresponding sides.

10 • 5 = (10 + d) • 2 Find the cross products.

50 = 20 + 2d Multiply. Subtract 20 from each side.

Use Indirect Measurement

Then divide each side by 2.

15 = d

Answer: The distance across the lake is 15 meters.

A. 12 feet

B. 27 feet

C. 30 feet

D. 45 feet

LAKES The two triangles shown in the figure are similar. Find the distance across the lake.

A. 2.1 feet

B. 33.3 feet

C. 75 feet

D. 300 feet

At the same time a 4-foot fencepost casts a 6-foot shadow, a cellular tower casts a 50-foot shadow. How tall is the cellular tower to the nearest tenth foot?

A. 1.5 feet

B. 18 feet

C. 24 feet

D. 66.6 feet

If the man in the picture is 6 feet tall, how tall is the tree?

A. 80 centimeters

B. 100 centimeters

C. 110 centimeters

D. 100 centimeters

A mother and daughter are standing next to each other. The mother is 160 centimeters tall and has a shadow that is 100 centimeters long. The daughter’s shadow is 50 centimeters long. How tall is the daughter?