In a triangle, angle C = 60 degrees AC = 10 BC = 5, find AB-?

Given:

AC = 10

BC = 5

Angle C = 60 °

Find AB.

To solve this problem, we use the formula of the cosine theorem, according to which the square of the side of a triangle is equal to the sum of the squares of its other two sides minus the double product of these sides by the cosine of the angle between them. Thus, for a triangle in which sides A, B, C and angle C are known, the following expression will be correct:

AB² = AC² + BC² – 2 * AC * BC * cos60 °.

Find AB:

AB² = 100 + 25 – 2 * 10 * 5 * 0.5 = 125 – 50 = 75

AB = √75 = 5√3

Answer: side AB is 5√3 (this is about 8.66 cm or, if rounded – 9 cm).