In △ABC, m∠A=35°, a=8, and b=10. Find c to the nearest tenth

Sounds like a great place to apply the Law of Cosines.

a^2 = b^2 + c^2 - 2 (a) (b) * cos (A) becomes:

8^2 = 10^2 + c^2 - 2 (8) (10) * cos 35 deg

Then:

64 = 100 + c^2 - 160 (0.819), or

-64 = c^2 - 131.06

Adding 131.06 to both sides, we get

67.06 = c^2. Taking the square root of both sides, we obtain c = 8.19. This should be rounded off to c = 8.2 (to the nearest tenth)