Question

In ️FGH, f=65 inches, g=48 inches and h=70 inches. find the measure of

Answer 1

Let's take a look at our triangle:

Using the law of cosines, we'll get that:

`G^2=F^2+H^2-2FH\cos \angle G`

Solving for angle G, we'll get:

`\begin{gathered} G^2=F^2+H^2-2FH\cos \angle G \\ \rightarrow2FH\cos \angle G^{}=F^2+H^2-G^2 \\ \rightarrow\cos \angle G=(F^2+H^2-G^2)/(2FH) \\ \\ \rightarrow\angle G=\cos ^(-1)(F^2+H^2-G^2)/(2FH) \end{gathered}`

This way,

`\begin{gathered} \angle G=\cos ^(-1)(65^2+70^2-48^2)/(2(65)(70)) \\ \\ \Rightarrow\angle G=41 \end{gathered}`