8.6 Law of Sines and Law of Cosines

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You used trigonometric ratios to solve right
triangles.
• Use the Law of Sines to solve triangles.
• Use the Law of Cosines to solve triangles.
• Law of Sines
• Law of Cosines
Law of Sines (AAS or ASA)
Find p. Round to the nearest tenth.
We are given measures of two angles and a
nonincluded side, so use the Law of Sines to write a
proportion.
Law of Sines (AAS or ASA)
Law of Sines
Cross Products Property
Divide each side by sin
Use a calculator.
Answer: p ≈ 4.8
Find c to the nearest tenth.
A. 4.6
B. 29.9
C. 7.8
D. 8.5
Law of Sines (ASA)
Find x. Round to the nearest tenth.
6
57°
x
Find x. Round to the nearest degree.
A. 8
B. 10
x
C. 12
D. 14
43°
Law of Cosines (SAS)
Find x. Round to the nearest tenth.
Use the Law of Cosines since the measures of two
sides and the included angle are known.
Law of Cosines (SAS)
Law of Cosines
Simplify.
Take the square root
of each side.
Use a calculator.
Answer: x ≈ 18.9
Find r if s = 15, t = 32, and mR = 40. Round to the
nearest tenth.
A. 25.1
B. 44.5
C. 22.7
D. 21.1
Law of Cosines (SSS)
Find mL. Round to the nearest degree.
Law of Cosines
Simplify.
Law of Cosines (SSS)
Subtract 754 from each side.
Divide each side by –270.
Solve for L.
Use a calculator.
Answer: mL ≈ 49
Find mP. Round to the nearest degree.
A. 44°
B. 51°
C. 56°
D. 69°
• Homework: Pg. 592 #’s 1 - 6
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