Ms. Cooper tells her geometry class to draw a triangle with with side lengths 4.2 cm and 3.0 cm with a 52° angle between them. What will be the measure of the third side?

One way to solve this (a SAS problem) is to use the Law of Cosines, which states:

c² = a² + b² + 2ab * cos (A),

where a and b are our known sides, angle A is our known angle, and c is the side we want to find

Plugging in:

c² = 4.2² + 3² + 2 (4.2) (3) (cos (52°)

c² = 17.64 + 9 + 25.2 (.62)

c² = 42.15

c = 6.5

Answer is 6.5 cm