Suppose a triangle has two sides of length 3 and 4 and that the angle between these two sides is pi/3. What is the length of the third side of the triangle?

We can use the Cosine Law (π / 3 = 60°):

c² = a² + b² - 2 a b cos C

c² = 4² + 3² - 2 · 4 ·3 · cos 60° = 16 + 9 - 24 · 1/2 = 25 - 12 = 13

Answer:

The length of the third side of a triangle is c = √ 13 ≈ 3.6