Right Triangles Calculator : The Pythagorean Theorem

Right Triangle
Calculate:
Enter:
a =
b =
c =
P =
s =
K =
ha =
hb =
hc =

Right Triangle Shape

Right Triangle Diagram with Angles A, B and C and sides opposite those angles a, b and c respectively
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
Right Triangle Diagram with Angles A, B and C and altitudes ha, hb and hc respectively

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

 

Cite this content, page or calculator as:

Furey, Edward "Right Triangles Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.