CK-12 Geometry-Concepts

8.10. Laws of Sines and Cosines http://www.ck12.org

sin 57◦

a

=

sin 85◦

b

=

sin 38◦

12

sin 57◦

a

=

sin 38◦

12

sin 85◦

b

=

sin 38◦

12

a·sin 38◦= 12 ·sin 57◦ b·sin 38◦= 12 ·sin 85◦

a=

12 ·sin 57◦

sin 38◦

≈ 16. 4 b=

12 ·sin 85◦

sin 38◦

≈ 19. 4

Example B

Solve the triangle using the Law of Sines. Round decimal answers to the nearest tenth.

Set up the ratio for^6 Busing Law of Sines.

sin 95◦

27

=

sinB

16

27 ·sinB= 16 ·sin 95◦

sinB=

16 ·sin 95◦

27

→sin−^1

(

16 ·sin 95◦

27

)

= 36. 2 ◦

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.