Find the missing side of a right triangle calculator

Right triangle

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Find the missing side of a right triangle calculator
 
Find the missing side of a right triangle calculator

[1]  2022/09/06 21:42   60 years old level or over / A retired person / Very /

Purpose of useHam radio antenna height calculation for a sloper antenna to operate on 60-meter and 17-meter ham bands.Comment/RequestChange top illustration according to the drop-down selection to show fixed and variables.

[2]  2022/08/18 06:48   30 years old level / High-school/ University/ Grad student / Useful /

Purpose of useLooking up formulas.Comment/RequestDefinitions of tan, sin, cos would be appreciated on this page.

[3]  2022/08/17 03:24   60 years old level or over / An office worker / A public employee / Useful /

Purpose of useWhat are the units of measure for a, b & h? It does not specify whether it is cm, m, in, or ft.from KeisanPlese read the FAQ page.

[4]  2022/07/13 16:45   30 years old level / An office worker / A public employee / Very /

Purpose of useEstimating size of thunderstorm system

[5]  2022/04/20 03:14   30 years old level / High-school/ University/ Grad student / Useful /

Purpose of useCalculating the angle of a slope

[6]  2022/03/06 08:30   20 years old level / Self-employed people / Very /

Purpose of useDetermining the distance between someone on top of a battlement and a person on the ground in a game of D&D.

[7]  2022/01/26 08:05   60 years old level or over / An office worker / A public employee / Very /

Purpose of useDetermine the average inclination angle (assumes constant slope) and actual distance traveled (hypotenuse) for an uphill hike of known horizontal distance and known elevation gain. Needed for planning a hike in which the slope is fairly constant and always uphill (> 0) on accent.

[8]  2021/10/20 13:21   20 years old level / A homemaker / Very /

Purpose of useCalculating the slope on a wheelchair ramp

[9]  2021/09/22 04:36   30 years old level / An office worker / A public employee / Useful /

Purpose of useFabricating desk legs and calculation of materials.

[10]  2021/07/07 17:48   30 years old level / An office worker / A public employee / Very /

Purpose of useTrying to recreate Thales of Milete's calculation of the height of the Great Pyramid with nothing but a stick and the sun.

Find the missing side of a right triangle calculator
 
Find the missing side of a right triangle calculator

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Pythagorean Theorem for Right Triangles

Find the missing side of a right triangle calculator

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 right triangle equals the length of the hypotenuse squared.

You might recognize this theorem in the form of the Pythagorean equation:

\[ a^{2} + b^{2} = c^{2} \]

If you know the length of any 2 sides of a right triangle you can use the Pythagorean equation formula to find the length of the third side.

Calculator Use

This calculator 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 right triangles only, enter any two values to find the third. See the solution with steps using the Pythagorean Theorem formula.

This calculator also finds the area A of the right triangle with sides a and b. The formula for area of a right triangle is:

\[ A = \dfrac {ab}{2} \]

Pythagorean Theorem Formula

Using the Pythagorean Theorem formula for right triangles you can find the length of the third side if you know the length of any two other sides. Read below to see solution formulas derived from the Pythagorean Theorem formula:

\[ a^{2} + b^{2} = c^{2} \]

Solve for the Length of the Hypotenuse c

The length of the hypotenuse is the square 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 square 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 area of a right triangle is side a multiplied by 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 + b2 = c2

The smallest known Pythagorean triple is 3, 4, and 5. Showing the work:

\[ a^{2} + b^{2} = c^{2} \] \[ 3^{2} + 4^{2} = 5^{2} \] \[ 9 + 16 = 25 \] \[ 25 = 25 \]

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 last accessed May 4, 2020.

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Find the missing side of a right triangle calculator
Find the missing side of a right triangle calculator

How do you find the missing side of a right triangle?

How to find the sides of a right triangle.
if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²).
if leg b is unknown, then. b = √(c² - a²).
for hypotenuse c missing, the formula is. c = √(a² + b²).

How do you find the third side of a right triangle?

The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c , Pythagoras' theorem states that: a² + b² = c² . To solve for c , take the square root of both sides to get c = √(b²+a²) .