right triangles and trigonometry chapter 8. pythagorean theorem a 2 + b 2 = c 2 right triangle a 2 +...

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Right Triangles Right Triangles and Trigonometry and Trigonometry Chapter 8 Chapter 8

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Page 1: Right Triangles and Trigonometry Chapter 8. Pythagorean Theorem a 2 + b 2 = c 2 right triangle a 2 + b 2 < c 2 obtuse triangle a 2 + b 2 > c 2 acute triangle

Right Triangles and Right Triangles and TrigonometryTrigonometry

Chapter 8Chapter 8

Page 2: Right Triangles and Trigonometry Chapter 8. Pythagorean Theorem a 2 + b 2 = c 2 right triangle a 2 + b 2 < c 2 obtuse triangle a 2 + b 2 > c 2 acute triangle

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

Page 3: Right Triangles and Trigonometry Chapter 8. Pythagorean Theorem a 2 + b 2 = c 2 right triangle a 2 + b 2 < c 2 obtuse triangle a 2 + b 2 > c 2 acute triangle

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

Page 4: Right Triangles and Trigonometry Chapter 8. Pythagorean Theorem a 2 + b 2 = c 2 right triangle a 2 + b 2 < c 2 obtuse triangle a 2 + b 2 > c 2 acute triangle

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

Page 5: Right Triangles and Trigonometry Chapter 8. Pythagorean Theorem a 2 + b 2 = c 2 right triangle a 2 + b 2 < c 2 obtuse triangle a 2 + b 2 > c 2 acute triangle

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

Page 6: Right Triangles and Trigonometry Chapter 8. Pythagorean Theorem a 2 + b 2 = c 2 right triangle a 2 + b 2 < c 2 obtuse triangle a 2 + b 2 > c 2 acute triangle

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

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