5.1 Special Right Triangles

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5.1 Special Right Triangles
You will be able to find the lengths of sides of
special right triangles
45-45-90 And 30-60-90
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Special Right Triangles
LegLegHypotenuse
Short LegLong LegHypotenuse
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In a 45-45-90 triangle
LEGS ARE THE SAME LENGTH
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45-45-90 Right Triangle
1
1
This is our reference triangle for the 45-45-90.
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45-45-90 Right Triangle
x
x
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EX 1 Solve for x
Lets set up a proportion by using our reference
triangle.
x
3
1
3
x
3
1
1
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EX 2 Solve for x
x
5
1
5
x
5
1
1
8
EX 3 Solve for x
x
3
45
3
1
1
1
x
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30-60-90
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30-60-90 Right Triangle
60
2
1
30
This is our reference triangle for the 30-60-90
triangle.
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30-60-90 Right Triangle
60?
2x
x
30?
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Ex 1
60
8
60
2
x
1
30
30
y
y
8
x
8
2
1
2
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Solve for x
Ex 2
30
60
2
x
1
24
60
30
x
24
2
1
2x 24
x 12
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Ex 3
30
60
2
14
1
y
30
60
x
y
14
x
2
14
2
1
2x 14
x 7
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Ex 4
x
60
2
1
60
30
30
y
x
y
1
2
y 10
x 5
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Classwork

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Homework
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