Question

Use the law of cosines to find “x” to the nearest whole number

Answer 1

The law of cosines states that

$\begin{gathered} c^2=a^2+b^2-2ab\cos\gamma \\ a,b,c\rightarrow\text{ sides of a triangle} \\ \gamma\rightarrow\text{ opposite angle to side c} \end{gathered}$

In our case,

$\begin{gathered} x=\sqrt{10^2+23^2-2*10*23\cos(135\degree)} \\ \Rightarrow x=\sqrt{629-460cos(135\degree)} \\ \Rightarrow x\approx30.89 \\ \Rightarrow x\approx31 \end{gathered}$

Once rounded, the answer is x=31