Help Solving Triangle !!?

Question

i need help solving this triangle !!

Side a = 120mm

Angle B = 33

Side c = 68mm

find:

angles A and C

and Side b

i've tried everything and I'm so stuck, please show steps !!!

Answer 1

b^2 = a^2+c^2 -2ac cos B = 120^2 +68^2 -2(120)(168)cos33=5336.9

b = sqrt(5336.9) = 73.1 mm.

sinA = asinB/b = 120sin33/73.1 = .8941

A = arcsin(.8941) = 63.4 degrees

C = 180 - 33 -63.4 = 83.6 degrees

Answer 2

alright....so basically you have to use the law of cosine which is:

c² = a² + b² − 2ab cos c

for this problem just make side a and side c as your ab and b as your c.

c² = 120^2 + 68^2 - 2(120)(68)cos33

Solve this out and you get: c = 73.05 that's your Side B. Then, now it becomes a little easier. Since you know all the sides of the triangle, you can use the law of sine which is:

sin A/ A = sin b/b

So you do: sin a/ 120 = sin 33/ 73.05 and you get angle A's angle  = 63.47

then you just add 63.47 + 33 to get 96.47. Subtract this from 180 and you get angle c which is 83.53