The Pythagorean Theorem
The Pythagorean theorem is [tex]a^2+b^2=c^2[/tex], where a and b are two legs of a right triangle and c is the hypotenuse (the longest side).
Solving the Question
We're given a triangle with the following:
- One of the legs measure 2 units
- The other leg measures b units
- The hypotenuse is 6 units long
We can plug these values into the Pythagorean theorem as a, b and c:
[tex]a^2+b^2=c^2\\2^2+b^2=6^2[/tex]
Now, isolate b:
[tex]b^2=6^2-2^2\\b=\sqrt{6^2-2^2}\\b=\sqrt{36-4}\\b=\sqrt{32}[/tex]
Answer
[tex]b=\sqrt{32}[/tex]
