Suppose a triangle has two sides of length 42 and 35, and that the angle between these two sides is 120 degrees. What is the length of the third side of the triangle?

Option D

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other and the given angle is the included angle. This means that the angle is formed by the intersection of the two lines. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:

b^2 = a^2 + c^2 - 2*a*c*cos (B).

The question specifies that a=42, B=120°, and c=35. Plugging in the values:

b^2 = 42^2 + 35^2 - 2 (42) (35) * cos (120°).

Simplifying gives:

b^2 = 4459.

Taking square root on the both sides gives b = 66.78 (rounded to the two decimal places).

This means that the length of the third side is 66.78 units!