Question

Suppose a triangle has two sides of length 33 and 37, and that the angle between these two sides is 120. What is the length of the third side of the triangle?
A. 55.70
B. 60.65
C. 43.64
D. 70

Answer 1

By cosine rule:

c² = a² + b² - 2abCosC

c² = 33² + 37² - 2*33*37Cos120

c² = 1089 + 1369 - 2442(-0.5)

c² = 3679

c = √3679

c ≈ 60.65

Option B.

Answer 2

Use the cosine law to answer the question which can be expressed as,
                           c² = a² + b² -2ab(cos C)
where c is the side opposite to angle C and a and b are the sides adjacent to the angle. Substituting the given values,
                             c² = 33² + 37² - (2)(33)(37)(cos 120°) = 3679
The value of c is 60.65. Therefore, the length of the third side is approximately 60.65 units.