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

Solution

Draw the diagram

So using cosine rule

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