Given a right triangle with: Side length = 4 and Hypotenuse = 5 Calculate the remaining side:

Pythagorean Theorem Formula

Side1^{2} + Side2^{2} = Hypotenuse^{2}

Solve for Side 2

Take the square root of both sides Side 1 = √Hypotenuse^{2} - Side 2^{2}

Plug in Hypotenuse = 5 and Side 2 = 4

Side 1 = √5^{2} - 4^{2} Side 1 = √25 - 16 Side 1 = √9

Final Answer

Side 1 = 3

What is the Answer?

Side 1 = 3

How does the Pythagorean Theorem Calculator work?

Free Pythagorean Theorem Calculator - Figures out based on user entry the missing side or missing hypotenuse of a right triangle. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem This calculator has 3 inputs.

What 3 formulas are used for the Pythagorean Theorem Calculator?

What 5 concepts are covered in the Pythagorean Theorem Calculator?

length

the measurement or extent of something from end to end

pythagorean theorem

a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides a^{2} + b^{2} = c^{2}

side

line segment joining two vertices in a polygon also known as an edge

theorem

A statement provable using logic

triangle

a flat geometric figure that has three sides and three angles

Example calculations for the Pythagorean Theorem Calculator