Transcript Indirect Measurement

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
Conversions
 You will need to know that 1 ft = 12 in
 Use a proportion to convert 40 inches into feet.
1ft xft
=
12in 40in
40 = 12x
X = 3.33 ft
Conversions
 Conversion factor- A numerical factor used to
multiply or divide a quantity when converting from
one system of units to another.
 Ex. 1 feet = 12 inches
 Ex. 5280 feet = 1 mile
 Ex. 1 cup = 8 ounces
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 inch
 Let’s make your shadow 12 inches longer than your height
 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. Attilio is 5 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 3-foot shadow. If
the pedestrian is 6 feet tall, how tall is the office
building?