how to find the sides of a right triangle
Pythagorean Theorem Calculator
Pythagorean Theorem for Right Triangles
a = side leg a
b = side leg b
c = hypotenuse
A = area
What is the Pythagorean Theorem?
The Pythagorean Theorem states that the sum of the squared sides of a correct triangle equals the length of the hypotenuse squared.
You might recognize this theorem in the class of the Pythagorean equation:
\[ a^{2} + b^{ii} = c^{ii} \]
If you know the length of any 2 sides of a correct triangle you can employ the Pythagorean equation formula to find the length of the tertiary side.
Calculator Use
This reckoner solves the Pythagorean Theorem equation for sides a or b, or the hypotenuse c. The hypotenuse is the side of the triangle opposite the right angle.
For correct triangles only, enter any ii values to find the tertiary. See the solution with steps using the Pythagorean Theorem formula.
This calculator also finds the expanse A of the right triangle with sides a and b. The formula for area of a right triangle is:
\[ A = \dfrac {ab}{two} \]
Pythagorean Theorem Formula
Using the Pythagorean Theorem formula for right triangles you tin notice the length of the 3rd side if y'all know the length of any two other sides. Read below to see solution formulas derived from the Pythagorean Theorem formula:
\[ a^{two} + b^{2} = c^{2} \]
Solve for the Length of the Hypotenuse c
The length of the hypotenuse is the foursquare root of the sum of the sides squared.
\[ c = \sqrt{a^{2} + b^{2}} \]
Solve for Length of Side a
The length of side a is the foursquare root of the squared hypotenuse minus the square of side b.
\[ a = \sqrt{c^{2} - b^{2}} \]
Solve for the Length of Side b
The length of side b is the square root of the squared hypotenuse minus the square of side a.
\[ b = \sqrt{c^{2} - a^{2}} \]
Solve for Area A of the Right Triangle
The expanse of a correct triangle is side a multiplied past side b divided by 2.
\[ A = \dfrac {ab}{2} \]
What are Pythagorean Triples?
A Pythagorean triple is a set of 3 positive integers for sides a and b and hypotenuse c that satisfy the Pythagorean Theorem formula a2 + btwo = ctwo
The smallest known Pythagorean triple is 3, four, and 5. Showing the work:
\[ a^{two} + b^{ii} = c^{ii} \] \[ 3^{2} + 4^{two} = 5^{two} \] \[ 9 + sixteen = 25 \] \[ 25 = 25 \]
References:
Weisstein, Eric W. "Pythagorean Theorem" From MathWorld--A Wolfram Web Resource. Pythagorean Theorem.
Wikipedia "Pythagorean Theorem" at https://en.wikipedia.org/wiki/Pythagorean_theorem terminal accessed May 4, 2020.
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