Transcript Special Right Triangles

Special Right Triangles
Section 8.3
45°- 45°- 90° Right triangles
• A special right triangle whose angles
are 45°, 45°and 90°. The lengths of the
sides of a 45°- 45°- 90° triangle are in
the ratio of 1: 1: 2
• In any 45-45-90
• The legs are equal
• The hypotenuse
• equals leg 2
Examples of 45-45-90 triangles
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Find x.
Write out the 3 sides with
the ratios
Leg: n = 8
Leg: n = 8
Hypotenuse:n 2  x
If n = 8, then the hypotenuse = 8 2
• Find x.
• Leg: n = x
• Leg: n = x
• Hypotenuse: n 2= 3 2
• Solve for n
3 2 n 2
3 2 n 2

2
2
• n = 3 so x = 3
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Solve for x
Leg:n = x
Leg:n = x
Hyp: n 2= 18
Solve for n
18  n 2
18 n 2

2
2
18 2
n
2
x 9 2
30-60-90 Triangles
• This is right triangle whose angles are 30°,
60°and 90°. The lengths of the sides of a
30°- 60°- 90° triangle are in the ratio of
1: 3 : 2
• Short leg across from 30
• Long leg across from 60
• Hypotenuse across from 90
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Solve for x and y
Short leg:n = 8
Long leg:n 3 = x
Hypotenuse: 2n = y
If n = 8 then
x=8 3
y = 2(8) = 16
•Solve for x and y
•Short leg: n = x
•Long leg: n 3 = 9 3
•Hypotenuse: 2n = y
•Solve for n to find x and y
•If n 3 = 9 3
n 3 9 3

3
3
n 9
x 9
3
y  2(9)
y  18
•Find x and y
•Short leg: n = x
•Long leg:n 3= 12
•Hyp: 2n = y
•Solve for n to find x and y.
•n 3 = 12
12
12 3
n4 3
n
n
3
3
•So x = 4 3 and y = 8 3