Question

Determine the value of A

Answer 1

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{4√(2)}\\ o=\stackrel{opposite}{a} \end{cases} \\\\\\ (9)^2= (4√(2))^2 + (a)^2\implies 81=4^2(2)+a^2\implies 81=32+a^2 \\\\\\ 49=a^2\implies √(49)=a\implies \boxed{7=a}`