In triangle ABC, sides a = 7 and b = 10 form an included angle C = 60°. Find side c to the nearest tenth.

We know two sides and the included angle, so the Law of Cosines is appropriate.

The Law of Cosines states:
c² = a² + b² - 2ab cos(C)

Substitute the known values:
c² = 7² + 10² - 2(7)(10)cos(60°)

Evaluate the squares:
c² = 49 + 100 - 140cos(60°)

We know:
cos(60°) = 1/2

Substitute:
c² = 149 - 140(1/2)

Simplify:
c² = 149 - 70
c² = 79

Take the positive square root because a side length must be positive:
c = √79

Using a calculator:
c ≈ 8.888

Round to the nearest tenth:
c ≈ 8.9

Therefore, side c is approximately 8.9 units long.