Triangle Calculator for Right Triangles
The Pythagorean Theorem

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:
ha = altitude of a
hb = altitude of b
hc = altitude of c

Notes and Formulas for Right Triangle Calculations:

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 a² + b² = c², better know 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 = √(a² + b²). Once we know sides a, b, and c we can calculate the perimeter = P, the semiperimeter = s, the area = K, and the altitudes: ha, hb, and hc. Let us know if you have any other suggestions!

Formulas and Calculations for a right triangle:

• Pythagorean Theorem for Right Triangle: a² + b² = c²
• 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: ha = b
• Altitude b of Right Triangle: hb = a
• Altitude c of Right Triangle: hc = (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, ha, hb, and hc
• c = √(a² + b²)
• P = a + b + c
• s = (a + b + c) / 2
• K = (a * b) / 2
• ha = b
• hb = a
• hc = (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, ha, hb, and hc
• b = √(c² - a²)
• P = a + b + c
• s = (a + b + c) / 2
• K = (a * b) / 2
• ha = b
• hb = a
• hc = (a * b) / c

For more information on right triangles see:

Weisstein, Eric W. "Right Triangle." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/RightTriangle.html

Weisstein, Eric W. "Altitude." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Altitude.html