Question

Use the Law of Cosines to determine the indicated side x. (Assume b = 25 and c = 50. Round your answer to one decimal place.)

Answer 1

The law of cosines can be written as:

`p^2=a^2+b^2-2\text{abCosP}`

Where

p, a, and b are the sides

P is the angle opposite of side p

Now,

x is what we want to find and other two sides given are 25 and 50 (let them be a and b)

Angle opposite to side unknown is 39 degrees, this is Angle P

Substituting, we get:

`\begin{gathered} p^2=a^2+b^2-2\text{abCosP} \\ x^2=25^2+50^2-2(25)(50)\text{Cos}39 \\ x^2=3125-2500Cos39 \\ x^2=3125-1942.86 \\ x=\sqrt[]{3125-1942.86} \\ x=34.38 \end{gathered}`