In triangle ABC a=5, b=7, and C=114.6 deg. solve the triangle.

c^2=5^2 + 7^2 - 2(5)(7)cos114.7
c^2= 74 - 70cos114.7
c=8.3

5^2=7^2+8.3^2 - 2(7)(8.3)cosA
25 = 117.89 - 116.2cosA
-92.89 = -116.2cosA
-92.89/-116.2 = 7.9939
cos^-1(7.9939) = 36.9

That means that angle B = 28.5, which is impossible.

Did I make a mistake anywhere?

Question

In triangle ABC a=5, b=7, and C=114.6 deg. solve the triangle.

c^2=5^2 + 7^2 - 2(5)(7)cos114.7
c^2= 74 - 70cos114.7
c=8.3

5^2=7^2+8.3^2 - 2(7)(8.3)cosA
25 = 117.89 - 116.2cosA
-92.89 = -116.2cosA
-92.89/-116.2 = 7.9939
cos^-1(7.9939) = 36.9

That means that angle B = 28.5, which is impossible.

Did I make a mistake anywhere?

anonymous · Answer

$ c = 10.1612 $

anonymous · Answer

$$\cos (114.7 ^\circ) = -0.417867 $$

anonymous · Answer

Thank you, don't have a graphing calculator with me.

anonymous · Answer

Glad to help :)