Question

question 4 of 25
suppose a triangle has two sides of length 42 and 35, and that the angle between these two sides is 120°. what is the length of the third side of the triangle?
a. 66.78
b. 43.65
c. 58.04
d. 77

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 42\), \(b = 35\), and \(C=120^{\circ}\).

Step2: Substitute the values

$$
LATEXBLOCK0
$$

Step3: Solve for \(c\)

\(c=\sqrt{4459}\approx66.78\)

Answer:

A. 66.78