Finding the Length of a Side in an Obtuse Triangle

Triangle DEF is an obtuse triangle, indicated by one angle measuring 120 degrees. The lengths of sides DE and DF are 10 cm and 7 cm, respectively.

What is the length of side EF, opposite the obtuse angle, and how does the Law of Cosines apply in this situation?

Recall that the Law of Cosines states:

c² = a² + b² - 2ab \\cos(C)

Where:

• c is the length of the side opposite the angle C (in this case, side EF).
• a and b are the lengths of the other two sides (DE and DF).
• C is the measure of the angle opposite side EF.