8.10. Laws of Sines and Cosines http://www.ck12.org
1.m^6 A
2.m^6 B
3.m^6 C
Answers:
- When you are given only the sides, you have to use the Law of Cosines to find one angle and then you can use the
Law of Sines to find another.
152 = 222 + 282 − 2 ( 22 )( 28 )cosA
225 = 1268 −1232 cosA
− 1043 =−1232 cosA
− 1043
− 1232=cosA→cos−^1(
1043
1232
)
≈ 32. 16 ◦
- Now that we have an angle and its opposite side, we can use the Law of Sines.
sin 32. 16 ◦
15=
sinB
22
15 ·sinB= 22 ·sin 32. 16 ◦sinB=22 ·sin 32. 16 ◦
15sin−^1
( 22 ·sin 32. 16 ◦
15)
≈ 51. 32 ◦.
- To findm^6 C, use the Triangle Sum Theorem.
32. 16 ◦+ 51. 32 ◦+m^6 C= 180 ◦
m^6 C= 96. 52 ◦Explore More
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