Question

For the given law of cosines equation solve for angle b round your answer to the nearest degree

Answer 1

Step 1

Given;

`12^2=(4.5)^2+10^2-2(4.5)(10)cosB`

Required; To find angle B

Step 2

`\begin{gathered} 4.5^2+10^2-90\cos\left(B\right)=12^2 \\ 20.25+100-90\cos\left(B\right)=12^2 \\ -90\cos\lparen B)+120.25=12^2 \\ -90\cos\left(B\right)+120.25=144 \\ \\ \end{gathered}`
`\begin{gathered} -90\cos\left(B\right)=23.75 \\ (-90\cos\left(B\right))/(-90)=(23.75)/(-90) \\ cos(B)=-(19)/(72) \\ B=\cos^(-1)(-(19)/(72)) \\ B=105.3009409^(\circ) \\ B\approx105^(\circ) \end{gathered}`

Answer;

`B=105^(\circ)\text{ to the nearest degree}`