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

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 226.552 ; ; b = 113.276 ; ; c = 196.2 ; ;

2. 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 ; ;

3. Semiperimeter of the triangle

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

4. 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 ; ;

5. 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 ; ;

6. 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 113.28**2+196.2**2-226.55**2 }{ 2 * 113.28 * 196.2 } ) = 90° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 226.55**2+196.2**2-113.28**2 }{ 2 * 226.55 * 196.2 } ) = 30° ; ;
 gamma = 180° - alpha - beta = 180° - 90° - 30° = 60° ; ;

7. Inradius

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

8. Circumradius

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

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 113.28**2+2 * 196.2**2 - 226.55**2 } }{ 2 } = 113.276 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 196.2**2+2 * 226.55**2 - 113.28**2 } }{ 2 } = 204.211 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 113.28**2+2 * 226.55**2 - 196.2**2 } }{ 2 } = 149.85 ; ;
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