A=10 b=3 C=15?

Question

round lengths to the nearest tenth and angle to to the nearest degree

Answer 1

If you are talking about a triangle, side a = 10, side b = 3, angle C= 15 degrees then by the law of cosines.

c^2 = a^2 + b^2 - ab cos C

c^2 = 100 + 9 - 30 (0.9659) 109-28.977 = 80.0

c = 8.9

Then in reverse a^2 = b^2 + c^2 - bc cos A

100= 9 + 80 - 3 x 8.9 cos A  (using the more exact version of c)

11 = -26.8 cos A (note the cosine has to be negative)

cos A = -11/26.83

A = arc cos - (0.40998) = 114 degrees

Leaving: 180 - 15 - 114 = B = 51 degrees

Note on the title to the question the a is capitalized but on the question page it is not.