Because the triangle in the picture is a right angle triangle, we can use the Pythagorean theorem to solve the unknown side.
The Pythagorean states that if you take the legs of a right triangle and square them and add them up, they will equal the hypotenuse squared.
In a mathematical equation: [tex]a^{2} + b^{2} = c^{2}[/tex]
In this problem, we know the length of one leg and we know the length of the hypotenuse.
The variables a and b in the equation [tex]a^{2} + b^{2} = c^{2}[/tex] are the legs. So, they are interchangeable. But the c variable is the hypotenuse.
Plug in the values.
[tex]6^{2} + b^{2} = \sqrt{117}^{2} [/tex]
Solve for b.
[tex]6^{2} + b^{2} = \sqrt{117}^{2} [/tex]
[tex]36+ b^{2} = \sqrt{117}^{2} [/tex]
[tex]36+ b^{2} = 117 [/tex]
[tex]b^{2} = 81 [/tex]
b = 9
So, the unknown side is 9 units long.
