Question

In XYZ, XY=14, YZ=22, and XZ=28. What is the measure of angle Z to the nearest degree? *Law of Cosines

Answer 1

Draw the diagram

So using cosine rule

`\begin{gathered} z^2=x^2+y^2-2xycosZ \\ \\ cosZ=(x^2+y^2-z^2)/(2xy) \\ \\ cosZ=(22^2+28^2-14^2)/(2(22)(28)) \\ \\ cosZ=(67)/(77) \\ \\ Z=30\degree\text{ \lparen to the nearest degree\rparen} \end{gathered}`