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

Sagot :

Let's take a look at our triangle:

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

[tex]G^2=F^2+H^2-2FH\cos \angle G[/tex]

Solving for angle G, we'll get:

[tex]\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=\frac{F^2+H^2-G^2}{2FH} \\ \\ \rightarrow\angle G=\cos ^{-1}\frac{F^2+H^2-G^2}{2FH} \end{gathered}[/tex]

This way,

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

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