SOLVING
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Find the missing side of the triangle.
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
We should find the leg of this right triangle, not the hypotenuse.
The hypotenuse, the longest side, is already given to us.
We can find it using Pythagoras' Theorem:
[tex]\Large\textbf{$a^2+b^2=c^2$}[/tex].
We know b and c, we need to find a.
[tex]\bf{a^2+9^2=15^2}[/tex] | square
[tex]\bf{a^2+81=225}[/tex] | subtract 81
[tex]\bf{a^2=144}[/tex] | square-root both sides
[tex]\bf{a=\pm12}[/tex]
And we should automatically cross out this extraneous solution of "a=-12", because side lengths can't be negative!
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{a=12}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
