Special Right Triangles

1
Special Right Triangles

• We make a living by what we get, but we make a
  life by what we give. -- Winston Churchill

• Chapter 8 Section 3
• Learning Goal Use properties of 45-45 -90 ,
  and
• 30 -60 -90 Triangles

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45-45-90 Triangles
x

• Special Right Triangle

45
d2 x2 x2
d
x
d2 2x2
Simplify
vd2 v 2x2
d xv 2
Three sides of lengths x, x, xv2
What did we learn about ratios of sides?
Ratio of a 45-45-90 triangle is
1 1 v2
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45-45-90 Triangles

• Find the missing side

6
a 4v2 cm
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45-45-90 Triangles
3
8
45
21
14
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Special Right Triangles
A 24.5 mm
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30-60-90 Triangles
Consider an equilateral ?
30
a2 (2x)2 x2
2x
2x
Simplify
a2 4x2 x2
a
a2 3x2
60
60
va2 v3x2
x
x
a xv3
Three sides of lengths x, 2x, xv3
Ratio of a 30-60-90 triangle is
Ratios of sides?
1 v3 2
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30-60-90 Triangles

• Find the missing sides

4
60
10
5
8v3 3
30
5v3
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30-60-90 Triangles
60
30
8
6
60
4v2
Find the Altitude of the ?
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Special Right Triangles
Refer to the figure. Find x and y.
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Special Right Triangles
The length of the diagonal of a square is
cm. Find the perimeter of the square.
60 cm
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Special Right Triangles
The side of an equilateral triangle measures 21
inches. Find the length of an altitude of the
triangle.
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Homework

• Special Right Triangles 45-45-90, 30-60-90