Applications of Similar Triangles
September 23, 2013
What's Going On?
It's a bird, its a plane, it's...
Applications of Similar Triangles
Practice Test
Learning Goal ­ I will be able to use similar triangles to solve
problems in real­world situations.
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Applications of Similar Triangles
September 23, 2013
F.F.M.
Date: _________
Name: _________
ΔGUI ~ ΔLBO
Determine the lengths of the missing sides.
L
I
5.7 cm
U
6.3 cm
8.8 cm
B
G
O
12.3 cm
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Applications of Similar Triangles
September 23, 2013
Shadows and Mirrors
Similar triangles can be used to
determine the heights of objects in the
real world!
All you need is a mirror or the sun and
something to measure with.
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Applications of Similar Triangles
September 23, 2013
Shadows and Mirrors
Imagine you are outside and you find a
cat stuck in a tree.
The cat asks you, "Is it safe for me to
jump from here?"
All you have is a mirror and your lucky
measuring tape.
How would you know if it's safe for the
cat to jump?!
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Applications of Similar Triangles
September 23, 2013
imilar
Triangles to the rescue!
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Applications of Similar Triangles
imilar
Triangles to the rescue!
September 23, 2013
Is it safe for me to
jump from here?
Let me check using
SIMILAR TRIANGLES!
Ugh.
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Applications of Similar Triangles
September 23, 2013
imilar
Triangles to the rescue!
Luckily I can see the TOP
OF THE TREE in my
trusty pocket mirror!
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Applications of Similar Triangles
September 23, 2013
imilar
Triangles to the rescue!
I also know that the angle between the ground
and my eyes is THE SAME as the angle
between the ground and the top of the tree!
x
x
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Applications of Similar Triangles
September 23, 2013
imilar
Triangles to the rescue!
And because the tree and I both make 90o
angles with the ground, we gots ourselves a
couple of similar triangles!
x
x
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Applications of Similar Triangles
September 23, 2013
imilar
Triangles to the rescue!
But you don't know
the length of any sides!
Don't I?
x
x
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Applications of Similar Triangles
September 23, 2013
imilar
Triangles to the rescue!
Alright Mathketeers, Similar Triangle Person and CatBert
need your help!
Help explain how you would find the height of the tree using
the pocket mirror and your lucky measuring tape.
x
x
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Applications of Similar Triangles
September 23, 2013
imilar
Triangles to the rescue!
x
x
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Applications of Similar Triangles
September 23, 2013
OH NO!
Similar Triangle Person's laser vision has destroyed
the mirror on this beautiful SUNNY day.
How will he figure out the height of the
tree now?
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Applications of Similar Triangles
September 23, 2013
imilar
Triangles to the rescue!
AGAIN!
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Applications of Similar Triangles
September 23, 2013
Hey CatBert, did you know that because
the sun is so far away from the earth that
the angle it makes with the vertical when it
hits any object is the same?
No.
I know I am stuck
in a tree though.
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Applications of Similar Triangles
September 23, 2013
You crazy cat!
We can actually use our shadows to figure
out how high up the tree you are!
I am intrigued.
Tell me more.
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Applications of Similar Triangles
September 23, 2013
Look at these triangles!
x
x
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Applications of Similar Triangles
September 23, 2013
Let me guess...
They are similar.
You know it CatBert!
x
x
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Applications of Similar Triangles
September 23, 2013
Alright Mathketeers, Similar Triangle Person
and CatBert need your help! Again!
Help explain how you know the triangles are
similar. Then figure out how you can find
the height of the tree using the shadows and
your lucky measuring tape.
x
x
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Applications of Similar Triangles
September 23, 2013
x
x
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Applications of Similar Triangles
September 23, 2013
Applications of Similar Triangles
Mirrors
You can use a pocket mirror to determine the height of an object. Just move forward or backwards until you can see the top of the object in the mirror. The angle of your line of sight (X) is the same as the angle from the mirror to the top of the object. Thus, similar triangles!
H
h
X
X
d
h
d
=
H
D
D
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Applications of Similar Triangles
September 23, 2013
A person stands 2.2 m from a mirror. They look at the mirror from a height of 1.8 m.
If the object they are looking at through the mirror is 4.9 m from the mirror, what is the height of the object?
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Applications of Similar Triangles
September 23, 2013
Applications of Similar Triangles
Shadows
You can use shadows to determine the height of an object. Because the sun is so far away from the earth, the angle that sun rays when they hit an object (A) is the same no matter how tall the object is. Thus, similar triangles!
A
H
A
h
s
S
h
s
=
H
S
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Applications of Similar Triangles
September 23, 2013
If Charma is standing outside at a height of 1.4 m with a shadow that is 3.7 m long looking at a tree that has a shadow with a length of 10.3 m, how tall is the tree?
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Applications of Similar Triangles
September 23, 2013
Practice Test
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