Math Problem Help?

Question

In an arbitrary triangle ABC, Side a =14 and angle A=50 degree. If angle B=70 degree, Find the length of side b and side c

Answer 1

OK, a triangle has a total of 180 degrees so angle C is 180 - (50 +70) = 180 - 120 = 60

Using the formula sin A/a = sin B/b = sin C / c

sin 50/14 = sin 70 / b
b sin 50 = 14 sin 70
b = 14 sin 70 / sin 50
b = about 17.173542356679484521363125314633

sin 50 / 14 = sin 60 / c
c sin 50 = 14 sin 60
c = 14 sin 60 / sin 50
c = about 15.827222247859905497585022514782

Answer 2

OK, first of all, angle C is 60 degrees.
Using the law of sines,

(sin 50)/14 = (sin 70)/b

Cross-multiply: b*(sin 50) = 14*(sin 70)
b = (14*sin 70)/(sin 50) = 17.173

Starting over to find side c:

(sin 50)/14 = (sin 60)/c

c = 14*sin60/(sin 50) = 15.827

Answer 3

c=15.8, b=17.18