Question

Suppose a triangle has two sides of length 42 and 35, and that the angle between these two sides is 120°. Which equation should you solve to find the length of the third side of the triangle?

Answer 1

Answer:

D is the correct answers

Step-by-step explanation:

If we know two sides and an included angle of any triangle, we can use law of cosines to find the unknown length of the third side

Answer 2

The correct option is D. $c^{2} =(42)^{2} +(35)^{2} -2(35)(42)cos120$.

Given  triangle has two sides of length 42 and 35, and angle between these two sides is 120°.

The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (S A S) or the lengths of the three sides (SSS) are known.

From this law ,we have $a^{2} =b^{2} +c^{2} -2 bc cos \alpha$ , here a is the length of side to be calculated and alpha is the angle between the known side.

So,here  $a^{2} =(42)^{2} +(35)^{2} -2(42)(35) cos120$, since angle between the known sides is 120°.

Hence the correct option is D. $c^{2} =(42)^{2} +(35)^{2} -2(35)(42)cos120$.

For more details on Law of cosine follow the link:

https://brainly.com/question/17289163