2 Answers

Chris Lindseth · Answer 1 · 2023-04-21T23:21:00+0000

SOLVING

$\Large\maltese\underline{\textsf{A. What is Asked}}$

Find the missing side of the triangle.

$\Large\maltese\underline{\textsf{B. This problem has been solved!}}$

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:

$\Large\textbf{$a^2+b^2=c^2$}$ .

We know b and c, we need to find a.

$\bf{a^2+9^2=15^2}$ | square

$\bf{a^2+81=225}$ | subtract 81

$\bf{a^2=144}$ | square-root both sides

$\bf{a=\pm12}$

And we should automatically cross out this extraneous solution of "a=-12", because side lengths can't be negative!

$\cline{1-2}$

$\bf{Result:}$

$\bf{a=12}$

$\LARGE\boxed{\bf{aesthetic\\ot1\theta\ell}}$