Question

Use the Law of Cosines to determine the indicated angle 0. (Assume a = 65.01, b = 36.38, and c = 42.05. Round your answer to two decimal places.)

Answer 1

a = 65.01, b = 36.38, and c = 42.05.

And it is required to find the measure of angle 0 which will be the angle B

Using the law of cosine

`\begin{gathered} b^2=a^2+c^2-2\cdot a\cdot c\cdot\cos B \\ \cos B=(a^2+c^2-b^2)/(2\cdot a\cdot c)=(65.01^2+42.05^2-36.38^2)/(2\cdot65.01\cdot42.05)=0.854 \\ \end{gathered}`
`\angle\emptyset=\angle B=\cos ^(-1)0.854=31.31`

the answer is rounded to two decimals