Question

c = √a² + b². This is the formula for the length of the hypotenuse c of a right triangle. Solve this formula for a.

Answer 1

To find a, we can simply do c squared minus b squared, and then find the square root of our result.

What is Pythagorean Theorem?

The Pythagorean Theorem is an evidence-based theory that in a right triangle, the two smaller sides (when squared), or what we call legs, add up to the biggest side (squared), which is what we identify as the hypotenuse. I’ll show an example because for some, it is better to show than verbally explain.

Let’s say I have the measurements 5 squared, 12 squared, and 13 squared. The hypotenuse here would be 13 squared because it is the largest side. This is important to look for when solving Pythagorean Theorem problems because if done incorrectly, you will come out with the wrong answer. Now that we know 13 squared is our hypotenuse, or c squared, we know that a squared (5 squared) and b squared (12 squared) must add up to it.

To find the squared value of any number, what we do is we multiply it by itself. So, for a squared, we would multiply 5 by 5. This gives us 25, which means that a squared is equal to 25. We can do the same for b squared; 12 x 12 = 144, so b squared is equal to 144. Now that we have our squared versions of our numbers, we can add them to verify that this is a right triangle. Does 144 + 25 = 169? Yes! Because this equation is true, we have the right triangle and its measurements solved!

The formula for solving for a is simple! Here are the steps:

Step 1: c squared minus b squared.

Step 2: Find the result of step 1, then find the square root of the result.

Step 3: The square root of the result is your answer!

If you need help, let me know and I will gladly assist you.

Answer 2

Answer:

a = sqrt(c^2 - b^2)

see image.

Step-by-step explanation:

If you square both sides of the equation, you get the Pythagorean Theorem back again.

c = sqrt(a^2 + b^2)

c^2 = a^2 + b^2

Solve for a means to get a all by itself on one side of the equation. Subtract b^2 and then take the square root. See image.