unit 7 part 2 special right triangles 30°, 60,° 90° ∆s 45°, 45,° 90° ∆s
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Unit 7 Part 2
Special Right Triangles30°, 60,° 90° ∆s45°, 45,° 90° ∆s
Special Right Triangles
In a 45-45-90 degrees right triangle both legs are congruent and the hypotenuse is the length of the leg times 2
45
45
1
1
45-45-90 Triangle
In a 45-45-90 triangle, the length of the hypotenuse is 2 times the length of one leg.
x
xx
Another way of stating the formula
Example
Determine the length of each side of the following 45-45-90 triangle.
5
45
45
1
1nw
Find the length of each side.
45
45
8 √28 2n
w
45
45
1
1
Find the length of each side.
The hypotenuse is 6 2
45
45
6 2
45
45
1
1
n
w
Find the length of each Variable
This is a 45-45-90 triangle.
x3
y
45
45
1
1
30-60-90 triangle
In a 30-60-90 right triangle this is the format.
3030
30
60
60
60
x 2x
x 1
1
2
2
Hypotenuse = 2
Adjacent to 30 =
Adjacent to 60 = 1
30-60-90 Triangles
In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg.
x
x 3
2x
30
60
Another way of stating the formula
Example
Determine the length of each side of the following 30-60-90 triangle.
16
30 30
6012
n
w
Find the length of each variable.
30
60y
x
5 √ 35 3
30
6012
Find the length of each side.
60
30
12n
w
30
60
2
1
Find the length of each variable.
30
60
10
rs
30
6012
30
60 45
45