SOLUTION: How do you solve the triangle when angle A is 84 degrees, side a is 12, and side c is 20?

Question 250789: How do you solve the triangle when angle A is 84 degrees, side a is 12, and side c is 20?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Solve the triangle means find a, b, c and then A, B, C. We know A = 84 a = 12 and c = 20.
Find C by law of sines:
12 / sin(84) = 20 / sin C -> Sin C = 20*sin(84)/12 ~ 20(.99452)/12 ~ 1.66 - -> C ~ 37.1 degrees.
Nw since you know 2 angles you find the third by 180 -A - C = B.
180 - 84 - 37.1 ~ 58.9 = B.
we can find b, again by using law of sines:
12/sin(84) = b / sin(58.9) - -> b = 12*sin(58.9)/sin(84) - -> b ~ 12(.85717) / .99452 ~ 10.34
a = 12
b = 10.34
c = 20
A = 84
B = 58.9
C = 37.1
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