8.7. Extension: Laws of Sines and Cosines http://www.ck12.org
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 ◦To Summarize
UseLawofSineswhengiven:
- An angle and its opposite side.
- Any two angles and one side.
- Two sides and the non-included angle.
UseLawofCosineswhengiven:
- Two sides and the included angle.
- All three sides.
Review Questions
Use the Law of Sines or Cosines to solve 4 ABC. If you are not given a picture, draw one. Round all decimal
answers to the nearest tenth.