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a

in

b

in

Hypotenuse

in

Area

in²

The right triangle calculator will determine the length of any side of a right triangle given the other two sides. It will also calculate the area of the triangle. The hypotenuse calculator is also useful for solving right triangles. We will answer the questions on how do we find the hypotenuse and how to find the area of a right triangle in the upcoming sections.

The hypotenuse calculator solves for the longest side of the right triangle, known as the hypotenuse. This side is opposite the right angle is can be solved by using the Pythagorean theorem and solves for the hypotenuse. In a right triangle with legs `a`

and `b`

with hypotenuse `c`

, the equation used is `a² + b² = c²`

. To solve for `c`

take the square root of both sides to get `c = √b²-a²`

. This extension of the Pythagorean theorem is not given the name "hypotenuse formula". The Pythagorean theorem calculator is also an excellent tool for calculating the hypotenuse.

For example, legs of the right triangle are `4`

and `7`

. What is the hypotenuse?

- Insert
`a`

and`b`

into the hypotenuse calculator equation. - Square
`a`

and`b`

. - Evaluate
`a² + b²`

- Take the square root to solve for
`c`

. - The square root will yield a positive and negative result. Since we are dealing with length, disregard the negative result.
- The right triangle calculator is suggested to check the answer.

The method for finding the area of a right triangle is quite simple. All that is needed is the length of the base and the height. In a right triangle the base and the height are the two sides which form the right angle. The formula is `Area = (1/2)base * height`

. If you don't know the base or the height, you can find it using the Pythagorean theorem. Use the right triangle calculator to check your calculations or calculate the area of triangles with sides that have larger or decimal value length.

Notice the sides of a triangle have a certain degree of gradient or slope. We can use a slope calculator to determine the slope of each side. The formula for slope if you wish to calculate by hand is

`(y₂ - y₁)/(x₂ - x₁)`

So if the coordinates are `(1,-6) and (4,8)`

, the slope of the segment is `(8 + 6)/(4 - 1) = 14/3`

. An easy way to determine if the triangle is right just knowing the coordinates is to see if the slopes of any two lines multiply to equal `-1`

There is an easy way to convert angles from radians to degrees and degrees to radians with the use of the angle conversion.

**If angle is in radians**

- Multiply by
`180/π`

**If angle is in degrees**

- Multiply by
`π/180`