Question

Find the cosine of

I dont know what else it wants me to say because it says that its to short to ask.

Answer 1

well, for the cosine of G we'll need the hypotenuse GH, so let's get it, Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{GH}\\ a=\stackrel{adjacent}{√(6)}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ GH=\sqrt{ (√(6))^2 + 1^2}\implies GH=√( 6 + 1 ) \implies GH=√( 7 ) \\\\[-0.35em] ~\dotfill`

`\cos(G )=\cfrac{\stackrel{adjacent}{√(6)}}{\underset{hypotenuse}{√(7)}}\implies \cos(G )=\cfrac{√(6)}{√(7)}\cdot \cfrac{√(7)}{√(7)}\implies \cos(G )=\cfrac{√(42)}{7}`