Question 708129
Jess,
you are not giving me enough information, but I hope I can guess.
To find the length of the third side, you need information about the angles.
My guess is that your triangle looks kind of like this:
{{{drawing(300,300,-3,77,-4,76,
triangle(0,0,75,0,0,73.485),
rectangle(0,0,3,3),locate(32,0,75),
locate(-3,35,x),locate(33,45,105)
)}}} That little square in the corner means that the sides measuring x and 75 are perpendicular, which means that is a right triangle.
Maybe the drawing shows that little square, or maybe the problem stated that it was a right triangle, and you just forgot to mention it.
In right triangles, the perpendicular sides are called the "legs" of the right triangle and the other, longer side is called the "hypotenuse".
The Pythagorean theorem says that the lengths of the legs, squared, add to the length of the hypotenuse squared.
In this case
{{{x^2+75^2=105^2}}} --> {{{x^2+5625=11025}}} --> {{{x^2=11025-5625}}} --> {{{x^2=5400}}}
The length {{{x}}} can be calculated as an approximate decimal number, or as an exact irrational number.
The approximate value is {{{73.5}}} (or {{{73.48}}} or {{{73.485}}} if you needed more decimal places).
The exact result is {{{x=sqrt(5400)}}} or {{{x=30sqrt(6)}}}
because {{{5400=900*6}}} so {{{sqrt(5400)=sqrt(900)*sqrt(6)=30*sqrt(6)}}}