Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Right scalene triangle.

Sides: a = 226.552   b = 113.276   c = 196.2

Area: T = 11112.37656
Perimeter: p = 536.028
Semiperimeter: s = 268.014

Angle ∠ A = α = 909.9998924039° = 90° = 1.57107944489 rad
Angle ∠ B = β = 309.9999999999° = 30° = 0.52435987756 rad
Angle ∠ C = γ = 600.0001075962° = 60° = 1.04771994291 rad

Height: ha = 98.10999999998
Height: hb = 196.2
Height: hc = 113.276

Median: ma = 113.2766184223
Median: mb = 204.2111315328
Median: mc = 149.8549993127

Inradius: r = 41.46219221383
Circumradius: R = 113.276

Vertex coordinates: A[196.2; 0] B[0; 0] C[196.2199787278; 113.276]
Centroid: CG[130.8799929093; 37.75986666666]
Coordinates of the circumscribed circle: U[98.1; 56.63878157775]
Coordinates of the inscribed circle: I[154.738; 41.46219221383]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 900.0001075961° = 90° = 1.57107944489 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 1209.999892404° = 120° = 1.04771994291 rad

Calculate another triangle




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 226.55 ; ; b = 113.28 ; ; c = 196.2 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 226.55+113.28+196.2 = 536.03 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 536.03 }{ 2 } = 268.01 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 268.01 * (268.01-226.55)(268.01-113.28)(268.01-196.2) } ; ; T = sqrt{ 123484891.48 } = 11112.38 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11112.38 }{ 226.55 } = 98.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11112.38 }{ 113.28 } = 196.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11112.38 }{ 196.2 } = 113.28 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 226.55**2-113.28**2-196.2**2 }{ 2 * 113.28 * 196.2 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 113.28**2-226.55**2-196.2**2 }{ 2 * 226.55 * 196.2 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 196.2**2-226.55**2-113.28**2 }{ 2 * 113.28 * 226.55 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11112.38 }{ 268.01 } = 41.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 226.55 }{ 2 * sin 90° } = 113.28 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.