# Right Triangles Calculator

## Right Triangle Shape

A = angle A

a = side a

B = angle B

b = side b

C = angle C

c = side c

K = area

P = perimeter

See Diagram Below:

*h*a = altitude of a

*h*b = altitude of b

*h*c = altitude of c

*Length units are for your reference only since the value of the resulting lengths will always be the same no matter what the units are.

## Calculator Use

A right triangle is a special case of a
triangle where 1 angle is equal to 90 degrees. In the case of a right triangle a^{2} + b^{2} = c^{2}. This formula is known as the Pythagorean Theorem.

In our calculations for a right triangle we only consider 2 known sides to calculate the other 7 unknowns. For example, if we know a and b we can calculate c using the Pythagorean Theorem. c = √(a^{2} + b^{2}). Once we know sides a, b, and c we can calculate the perimeter = P, the semiperimeter = s, the area = K, and the altitudes:
*h*a, *h*b, and *h*c.
Let us know if you have any other suggestions!

### Formulas and Calculations for a right triangle:

- Pythagorean Theorem for Right Triangle: a
^{2}+ b^{2}= c^{2} - Perimeter of Right Triangle: P = a + b + c
- Semiperimeter of Right Triangle: s = (a + b + c) / 2
- Area of Right Triangle: K = (a * b) / 2
- Altitude a of Right Triangle:
*h*a = b - Altitude b of Right Triangle:
*h*b = a - Altitude c of Right Triangle:
*h*c = (a * b) / c

### 1. Given sides a and b find side c and the perimeter, semiperimeter, area and altitudes

- a and b are known; find c, P, s, K,
*h*a,*h*b, and*h*c - c = √(a
^{2}+ b^{2}) - P = a + b + c
- s = (a + b + c) / 2
- K = (a * b) / 2
*h*a = b*h*b = a*h*c = (a * b) / c

### 2. Given sides a and c find side b and the perimeter, semiperimeter, area and altitudes

- a and c are known; find b, P, s, K,
*h*a,*h*b, and*h*c - b = √(c
^{2}- a^{2}) - P = a + b + c
- s = (a + b + c) / 2
- K = (a * b) / 2
*h*a = b*h*b = a*h*c = (a * b) / c

For more information on right triangles see:

Weisstein, Eric W. "Right Triangle." From
*MathWorld*--A Wolfram Web Resource.
Right Triangle.

Weisstein, Eric W. "Altitude." From
*MathWorld*--A Wolfram Web Resource.
Altitude.

**Cite this content, page or calculator as:**

Furey, Edward "Right Triangles Calculator" at https://www.calculatorsoup.com/calculators/geometry-plane/triangles-right.php from CalculatorSoup,
*https://www.calculatorsoup.com* - Online Calculators

Last updated: October 3, 2023