Question

Pythagorean Theorem FormulaShow all steps to solve for each variable.

Answer 1

The formula of the Pythagorean theorem is

`\begin{gathered} a^2+b^2=c^2 \\ \text{ Where a and b are the legs and} \\ \text{c is the hypotenuse of the right triangle} \end{gathered}`

Graphically

So, to find the value of x you have:

`\begin{gathered} a=9 \\ b=5 \\ c=x \\ 9^2+5^2=x^2 \\ 81+25=x^2 \\ 106=x^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{106}=\sqrt[]{x^2} \\ 10.3=x \end{gathered}`

Now, to find the value of y you have:

`\begin{gathered} a=3 \\ b=5 \\ c=y \\ 3^2+5^2=y^2 \\ 9+25=y^2 \\ 34=y^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{34}=\sqrt[]{y^2} \\ \text{5}.8=y \end{gathered}`

Therefore, the values of the variables are

`\begin{gathered} x=10.3 \\ y=5.8 \end{gathered}`