Unit 6: Scale Factor and Measurement

Report
Unit 6: Scale Factor and
Measurement
How will you measure up?
What am I Learning Today?
Indirect Measurement
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
Tower is? Is there a way to find out
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? What
ideas do you have for
determining its height?
Questions
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 similarities
2) Create a proportion substituting values for the
given measurements
3) Solve for X
Use the similar triangles to find the
height of the tree.
6
3
__
__
=
h
9
Write a proportion using corresponding
sides.
h • 3 = 6 • 9 The cross products are equal.
3h = 54
3h
54
___
___
3 = 3
h is multiplied by 3.
Divide both sides
by 3 to undo
multiplication.
h = 18
The tree is 18 feet tall.
6 ft.
h
3 ft.
9 ft.
Measurement Application
A 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?
h
91.5 Write a proportion using
__
____
=
corresponding sides.
4
3
4 • 91.5 = h • 3 The cross products are equal.
366 = 3h
h is multiplied by 3.
366 = ___
3h Divide both sides by
___
3 to undo
3
3
multiplication.
122 = h
The rocket is 122 feet tall.
1. Use the similar triangles to find the height of the
post.
x
20 feet
8
ft
15 ft
6 ft
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?
25 feet
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?
1.8 meters
Measuring the Oddities of America




Measure your height to the nearest quarter
inch
Measure your shadow to the nearest
quarter inch
Using this information, determine the
heights or shadow lengths of the following
large immeasurable objects
Create proportions and solve for the
missing piece of information
The Jolly Green Giant
This monument found in
Blue Earth, Minnesota
stands a proud 55 feet
tall.
Using your height and
shadow length, find the
length of the Jolly Green
Giant’s shadow?
The World’s Tallest Man
Robert Pershing Wadlow was
(and still is) the tallest
human being ever
recorded.
He reached 8' 11" (272 cm)
in height and 490 pounds
(222.26 kg) in weight
before his death at the age
of 22.
What would have been the
length of his shadow
compared to yours?
World’s Tallest Snow Woman
Built in Bethel, Maine,
Olympia Snow Woman
took 28 days and 13
million pounds of snow to
construct. She has a
shadow of 61 feet long.
How tall is this snow
woman?
The World’s Tallest Arcade Game
This arcade machine
stands 13 feet tall,
has a 70 inch screen,
and plays vintage
video games. It casts
a shadow of 6.5 feet.
If Ms. Atkinson is 5.167
feet tall, how long
would her shadow be
in comparison?
Exit Ticket
Draw a sketch to represent each problem.
Set up the proportion and solve. Be sure to label
your answer.
A flagpole casts a shadow that is 9 feet. An
office building casts a shadow that is 15 feet.
If the building is 60 feet tall, how tall is the
flagpole?
An office building casts a 150-foot shadow at
the same time a nearby pedestrian casts a 3foot shadow. If the pedestrian is 6 feet tall,
how tall is the office building?

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