SOLUTION: In triangle ABC, C = 60 degrees, a = 12, and b= 5. Find c. a. 109.0 b. 10.4 c. 11.8 d. 15.1

Question 343975: In triangle ABC, C = 60 degrees, a = 12, and b= 5. Find c.
a. 109.0
b. 10.4
c. 11.8
d. 15.1
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
In triangle ABC, C = 60 degrees, a = 12, and b= 5. Find c.
a. 109.0
b. 10.4
c. 11.8
d. 15.1

are a and b 2 of the sides?

is c one of the sides?

is this a right triangle?

maybe you should repost

if this is right triangle:
then angles would be 30-60-90,
angle C would be the 60, angle B would be the 30, angle A would be the 90,
side c opposite angle C, side b = 5, side a = 12
pythagorean theorem: b^2 + c^2 = a^2 --> 5^2 + c^2 = 12^2
b^2 + c^2 = a^2 --> 5^2 + c^2 = 12^2 = c^2 + 25 = 144
c^2 = 119
c = sqrt(119) = 10.9087 to 4 places

if this is not a right triangle:
if angle C of 60 is the side opposite, and a and b are the 2 known sides:
use law of cosines: c^2 = a^2 + b^2 - 2abcosC
c^2 = 12^2 + 5^2 - 2 * 12 * 5 * cos 60
c^2 = 144 + 25 - 120cos60
c^2 = 169 - 120 * 0.5
c^2 = 169 - 60 = 109
c = sqrt(109) = 10.4403 rounded to 4 places
well this would match up with answer b. 10.4

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