Unit 6: Scale Factor and Unit 6: Scale Factor and MeasurementMeasurement

How will you measure up?How will you measure up?

Indirect MeasurementIndirect MeasurementWhat am I Learning Today?What am I Learning Today?

How will I show that I learned it?How will I show that I learned it?Demonstrate the relationship between

similar plane figures using ratio and proportion

Use proportions and similar figures to find unknown measures

Solve real world problems using indirect measurement

Do you know how tall the Eiffel Do you know how tall the Eiffel Tower is? Is there a way to find out Tower is? Is there a way to find out

without actually measuring it?without actually measuring it? What I do know is that on a sunny

day, its shadow is 328 feet long.

What could we do to solve this problem? Whatideas do you have fordetermining its height?

Questions AnswersQuestions Answers

What is indirect measurement?

A technique that uses proportions to find a measurement when it is not possible to measure something directly.

How can I find the length or

height without using standard

measuring tools?

Use similar figures and proportions:1) Draw a sketch to identify similarities2) Create a proportion substituting values for the

given measurements3) Solve for X

Use the similar triangles to find the Use the similar triangles to find the height of the tree.height of the tree.

3 9

__ 6 h

__ =

h • 3 = 6 • 9

3h = 54

3h 3

___ 54 3

___ =

h = 18

Write a proportion using corresponding sides.

The cross products are equal.

h is multiplied by 3.

Divide both sides by 3 to undo multiplication.

The tree is 18 feet tall.

3 ft. 9 ft.

6 ft. h

Measurement ApplicationA rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket?

91.5 3

____ h 4

__ =

4 • 91.5 = h • 3 366 = 3h

366 3

___ 3h 3

___ =

122 = h

Write a proportion using corresponding sides.The cross products are equal.

h is multiplied by 3.Divide both sides by 3 to undo multiplication.

The rocket is 122 feet tall.

1. Use the similar triangles to find the height of the post.

2. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost?

3. A stop sign casts a shadow 8 meters long, while a bush nearby casts a shadow 4.5 meters long. If the stop sign is 3.2 meters high, how tall is the bush?

25 feet

20 feet8 ft

6 ft

x

15 ft

1.8 meters

Measuring the Oddities of AmericaMeasuring the Oddities of America Measure your height to the nearest Measure your height to the nearest

quarter inchquarter inch Measure your shadow to the nearest Measure your shadow to the nearest

quarter inch quarter inch Using this information, determine the Using this information, determine the

heights or shadow lengths of the heights or shadow lengths of the following large immeasurable objectsfollowing large immeasurable objects

Create proportions and solve for the Create proportions and solve for the missing piece of informationmissing piece of information

The Jolly Green GiantThe Jolly Green Giant

This monument found This monument found inin

Blue Earth, MinnesotaBlue Earth, Minnesotastands a proud 55 feetstands a proud 55 feet

tall.tall.

Using your height and Using your height and shadow length, find the shadow length, find the

length of the Jolly length of the Jolly Green Giant’s shadow?Green Giant’s shadow?

The World’s Tallest ManThe World’s Tallest ManRobert Pershing Wadlow Robert Pershing Wadlow

was (and still is) the was (and still is) the tallest human being tallest human being

ever recorded. ever recorded. He reached 8' 11" (272 He reached 8' 11" (272

cm) in height and 490 cm) in height and 490 pounds (222.26 kg) in pounds (222.26 kg) in

weight before his death weight before his death at the age of 22.at the age of 22.

What would have been What would have been the length of his shadow the length of his shadow

compared to yours?compared to yours?

World’s Tallest Snow WomanWorld’s Tallest Snow WomanBuilt in Bethel, Maine,Built in Bethel, Maine,Olympia Snow WomanOlympia Snow Womantook 28 days and 13took 28 days and 13

million pounds of snow million pounds of snow toto

construct. She has aconstruct. She has ashadow of 61 feet long.shadow of 61 feet long.

How tall is this snow How tall is this snow woman?woman?

The World’s Tallest Arcade GameThe World’s Tallest Arcade GameThis arcade machineThis arcade machine

stands 13 feet tall, stands 13 feet tall, has a 70 inch screen,has a 70 inch screen,

and plays vintageand plays vintagevideo games. It castsvideo games. It castsa shadow of 6.5 feet.a shadow of 6.5 feet.

If Ms. Atkinson is 5.167 If Ms. Atkinson is 5.167 feet tall, how long feet tall, how long

would her shadow be would her shadow be in comparison?in comparison?

Exit TicketExit TicketDraw a sketch to represent each problem.Draw a sketch to represent each problem.Set up the proportion and solve. Be sure to Set up the proportion and solve. Be sure to

label your answer.label your answer.

A flagpole casts a shadow that is 9 feet. An A flagpole casts a shadow that is 9 feet. An office building casts a shadow that is 15 office building casts a shadow that is 15 feet. If the building is 60 feet tall, how feet. If the building is 60 feet tall, how tall is the flagpole?tall is the flagpole?

An office building casts a 150-foot shadow An office building casts a 150-foot shadow

at the same time a nearby pedestrian at the same time a nearby pedestrian casts a 3-foot shadow. If the pedestrian is casts a 3-foot shadow. If the pedestrian is 6 feet tall, how tall is the office building?6 feet tall, how tall is the office building?