8.10. Laws of Sines and Cosines http://www.ck12.org
To findm^6 Cuse the Triangle Sum Theorem.m^6 C+ 95 ◦+ 36. 2 ◦= 180 ◦→m^6 C= 48. 8 ◦
To findc, use the Law of Sines again.sin 95
◦
27 =
sin 48. 8 ◦
c
c·sin 95◦= 27 ·sin 48. 8 ◦
c=
27 ·sin 48. 8 ◦
sin 95◦
≈ 20. 4
Example C
Solve the triangle using Law of Cosines. Round your answers to the nearest hundredth.
Use the second equation to solve for^6 B.
b^2 = 262 + 182 − 2 ( 26 )( 18 )cos 26◦
b^2 = 1000 −936 cos 26◦
b^2 = 158. 7288
b≈ 12. 60
To findm^6 Aorm^6 C, you can use either the Law of Sines or Law of Cosines. Let’s use the Law of Sines.
sin 26◦
12. 60
=
sinA
18
12. 60 ·sinA= 18 ·sin 26◦
sinA=
18 ·sin 26◦
12. 60
sin−^1
( 18 ·sin 26◦
12. 60
)
≈ 38. 77 ◦To findm^6 C, use the Triangle Sum Theorem.
26 ◦+ 38. 77 ◦+m^6 C= 180 ◦
m^6 C= 115. 23 ◦
Watch this video for help with the Examples above.
MEDIA
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CK-12 Foundation: Chapter8LawsofSinesandCosinesB
Vocabulary
TheLaw of SinessayssinaA=sinbB=sincCfor any triangle (including non-right triangles). TheLaw of Cosinessays
a^2 =b^2 +c^2 − 2 bccosAfor any triangle.