Question

I’m confused how to do this

Answer 1

let's notice that is a right-triangle, and the other two angles are twins of 45°, namely that the "legs" are twins as well, so if the vertical/opposite one is "x" units long, then the horizontal/adjacent is also "x" units long.

so let's use the pythagorean theorem for that then.

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies (√(7))^2=x^2+x^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{√(7)}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{x}\\ \end{cases} \\\\\\ 7=2x^2\implies \cfrac{7}{2}=x^2\implies \sqrt{\cfrac{7}{2}}=x\implies \cfrac{√(7)}{√(2)}=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{now, let's \underline{rationalize} the denominator}}{\cfrac{√(7)}{√(2)}\cdot \cfrac{√(2)}{√(2)}\implies \cfrac{√(14)}{2}}`