Suppose a triangle has two sides of lengths 2 and 5 and that the angle between these two sides is 60 degrees. What is the length of the third side of the triangle?
We are given two sides and an angle in between the two sides.
Recognize this?
Side-Angle-Side.
We can use the Law of Cosines to calculate the missing side.
\(c^{2} = 2^2 + 5^2 - 2 * 2 * 5 * cos(60)
c^2 = 4+25-20*cos(60)\)
\(c^2 = 4+25-20*cos(60)\)
\(c^2 = 19\)
\(c = \sqrt{19}\)