[tex]\tt Step-by-step~explanation:[/tex]
To be able to solve this question, we need to know about the Pythagorean theorem: a² + b² = c². A and b represents the two sides that make the right angle, and C represents the hypotenuse, or the longest side, of the triangle.
[tex]\tt Step~1:[/tex]
We know that the hypotenuse is the longest side of the triangle, so that means 9 is c. One side of the triangle is 6, and we have to solve for b. That means 6 is a. We can plug in our values to the formula like this:
[tex]\tt a^2+b^2=c^2\\6^2+b+2=9^2\\36+b^2=81[/tex]
[tex]\tt Step~2:[/tex]
Now that we have our equation down, we know what we have to do next: subtract 81 from 36 to get b².
[tex]\tt 81-36=\sqrt{45}[/tex]
[tex]\Large\boxed{\tt Our~final~answer:~b=\sqrt{45} ~(simplified:3\sqrt{5}) }[/tex]
