right triangles and trigonometry chapter 8. pythagorean theorem a 2 + b 2 = c 2 right triangle a 2 +...
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Right Triangles and Right Triangles and TrigonometryTrigonometry
Chapter 8Chapter 8
Pythagorean TheoremPythagorean Theorem
aa22 + b + b22 = c = c22 right triangleright triangle
aa22 + b + b22 < c < c2 2 obtuse triangleobtuse triangle
aa22 + b + b22 > c > c22 acute triangle acute triangle
a
b
c
Example of Using the Example of Using the Pythagorean TheoremPythagorean Theorem
222 208 x40064 2 x
3362 x
D
EF
820
x
-64 -64
3362 x
214x
In a 45º-45º-90º triangle, both legs are congruent and the length of the hypotenuse is times the length of a leg.
4545º-45º-90º Triangle Theoremº-45º-90º Triangle Theorem
2
2sS
S
2shyp
3030º-60º-90º Triangle Theoremº-60º-90º Triangle Theorem
In a 30In a 30º-60º-90º triangle, the length of the º-60º-90º triangle, the length of the hypotenuse is twice the length of the shorter hypotenuse is twice the length of the shorter leg. The length of the longer leg is leg. The length of the longer leg is times the length of the shorter leg. times the length of the shorter leg.
3
30º
60º
2s
s
3s
hyp. = 2 • short side
long side = • short side3
Trigonometry RatiosTrigonometry Ratios
Hypotenuse
Opposite
Hypotenuse
Adjacent
Adjacent
Opposite
Sine =
Cosine =
Tangent =
P
Q
R
q
pP sin
p
q
r
q
rP cos
r
pP tan