LAW OF SINES

The law of sines is only used in a non-right triangle when you have a "pair" (an angle and it's opposite side)

FORMULA: (sinA / a) = (sinB / b) = (sinC / c)

*hint* cross multiply to solve*

You get two answers for inverses --> you must check to see if they work

Example 1: angle A = 52 degrees, a = 3, and angle C = 63 degrees. Find b, c, and B please.

Well since you asked nicely...

All triangles equal 180 degrees so...

180 -52 -63= B

B = 65 degrees

(sin 52) / 3 = (sin 65) / b

3 (sin 65) = b (sin52)

b=3 (sin 65) / (sin 52)

b = 3.45

(sin 52) / 3 = (sin 63) / c

3 (sin 63) = c (sin 52)

c = 3 (sin 63) / (sin 52)

c = 3.392

Example 2: a = 8, b = 2, c = 6, angle A = 100. Find B and C now!

(sin 100) / 8 = (sin B) / 2

2sin 100 = 8 sin B

sin B = 2(sin 100) / 8

B = arcsin ( 2(sin 100) / 8)

B = 14.253 degrees, 165.747 degrees but here 165.747 doesn’t work.

180 -100 -14.253 = C

C = 65.747 degrees