Question

a. The lengths of two sides of a triangle are 8 and 10 , and the measure of the angle between them is 40°. What is the approximate length of the third side?

Answer 1

6.437

Explanation:

By the Law of Cosines, if we let the length of the third side be x,

`x^2 = 8^2 + 10^2 - 2(8)(10)\cos 40^(\circ) \\ \\ x=\sqrt{8^2 + 10^2 - 2(8)(10)\cos 40^(\circ)} \\ \\ x \approx 6.437`