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marta [7]
4 years ago
10

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 t

he third side of the triangle?
A. 55.70
B. 60.65
C. 43.64
D. 70
Mathematics
2 answers:
Daniel [21]4 years ago
7 0
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.
postnew [5]4 years ago
6 0
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. 
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