Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 223   b = 300   c = 500

Area: T = 18945.22878935
Perimeter: p = 1023
Semiperimeter: s = 511.5

Angle ∠ A = α = 14.63216002266° = 14°37'54″ = 0.25553695988 rad
Angle ∠ B = β = 19.86661951594° = 19°51'58″ = 0.34767305154 rad
Angle ∠ C = γ = 145.5022204614° = 145°30'8″ = 2.53994925394 rad

Height: ha = 169.9122357789
Height: hb = 126.302151929
Height: hc = 75.78109115741

Median: ma = 396.9488044459
Median: mb = 356.8821633038
Median: mc = 85.81766650482

Inradius: r = 37.03985687068
Circumradius: R = 441.4044033089

Vertex coordinates: A[500; 0] B[0; 0] C[209.729; 75.78109115741]
Centroid: CG[236.5766333333; 25.2660303858]
Coordinates of the circumscribed circle: U[250; -363.7822243145]
Coordinates of the inscribed circle: I[211.5; 37.03985687068]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.3688399773° = 165°22'6″ = 0.25553695988 rad
∠ B' = β' = 160.1343804841° = 160°8'2″ = 0.34767305154 rad
∠ C' = γ' = 34.4987795386° = 34°29'52″ = 2.53994925394 rad

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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 = 223 ; ; b = 300 ; ; c = 500 ; ;

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

p = a+b+c = 223+300+500 = 1023 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1023 }{ 2 } = 511.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 511.5 * (511.5-223)(511.5-300)(511.5-500) } ; ; T = sqrt{ 358921659.94 } = 18945.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18945.23 }{ 223 } = 169.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18945.23 }{ 300 } = 126.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18945.23 }{ 500 } = 75.78 ; ;

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{ 223**2-300**2-500**2 }{ 2 * 300 * 500 } ) = 14° 37'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 300**2-223**2-500**2 }{ 2 * 223 * 500 } ) = 19° 51'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 500**2-223**2-300**2 }{ 2 * 300 * 223 } ) = 145° 30'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18945.23 }{ 511.5 } = 37.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 223 }{ 2 * sin 14° 37'54" } = 441.4 ; ;




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