Special Right Triangles. Draw 5 squares with each side length increasing by 1 1 2 3 4 5.
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Transcript of Special Right Triangles. Draw 5 squares with each side length increasing by 1 1 2 3 4 5.
Find the length of each diagonal1
2
3
4
a2 + b2 = c2 42 + 42 = c2
16 + 16 = c2
32 = c2
32 = c 4 2 = c
Find the length of each diagonal1
2
3
4
5a2 + b2 = c2 52 + 52 = c2
25 + 25 = c2
50 = c2
50 = c 5 2 = c
Now, what do you know about squares and the triangle formed by
the diagonal.
• A square has 4 equal sides and 90° angles•The triangle is isosceles right
45-45-90 triangles follow the same pattern we found in the squares.
45°
45°
a
a 2
So if you know one side you can find the other.
There is a second “special right triangle”…30-60-90
Obviously if one angle is 30° then the other is 60°
30°
Angle Sum of Triangle
Draw five 30-60-90 trianglesEach short leg increasing by 1
30°
10
5
30°
8
4
30°6
3
30°
4
2
30°
2
1
Find the long legb
b
b
b b
Find the long leg
a2 + b2 = c2 22 + b2 = 42
4 + b2 = 16 b2 = 16-4 b2 = 12 b = 12 b = 2 3
30°
4
2
30°
2
1
b
b
Find the long leg
a2 + b2 = c2 32 + b2 = 62
9 + b2 = 36 b2 = 36-9 b2 = 27 b = 27 b = 3 3
30°
4
2
30°
2
1
b
b30°6
3
b
Find the long leg
a2 + b2 = c2 42 + b2 = 82
16 + b2 = 64 b2 = 64-16 b2 = 48 b = 48 b = 4 3
30°
4
2
30°
2
1
b
b30°6
3
b 30°
8
4
b
Find the long leg30°
4
2
30°
2
1
b
b30°6
3
b 30°
8
4
b 30°
10
5
b
a2 + b2 = c2 52 + b2 = 102
25 + b2 = 100 b2 = 100-25 b = 75 b = 5 3
Do you see the pattern?
30°
2
30°
130°
3
3 3 30°
4
4 3
30°
5
5 3
2 3
3
Long leg = short leg time the square root of 3