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 = 193.19327   b = 64.41   c = 182.13994

Area: T = 5865.7999377
Perimeter: p = 439.74221
Semiperimeter: s = 219.871105

Angle ∠ A = α = 900.0000249101° = 90° = 1.57107967616 rad
Angle ∠ B = β = 19.47551317532° = 19°28'30″ = 0.34399051714 rad
Angle ∠ C = γ = 70.52548433367° = 70°31'29″ = 1.23108907207 rad

Height: ha = 60.72548553077
Height: hb = 182.13994
Height: hc = 64.41

Median: ma = 96.59663235991
Median: mb = 184.9654667323
Median: mc = 111.5455252963

Inradius: r = 26.67883615988
Circumradius: R = 96.596635

Vertex coordinates: A[182.13994; 0] B[0; 0] C[182.1399428003; 64.41]
Centroid: CG[121.4266276001; 21.47]
Coordinates of the circumscribed circle: U[91.07697; 32.20550395937]
Coordinates of the inscribed circle: I[155.461105; 26.67883615988]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 909.9999750899° = 90° = 1.57107967616 rad
∠ B' = β' = 160.5254868247° = 160°31'30″ = 0.34399051714 rad
∠ C' = γ' = 109.4755156663° = 109°28'31″ = 1.23108907207 rad

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How did we calculate this triangle?

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

a = 193.193 ; ; b = 64.41 ; ; c = 182.139 ; ;

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

p = a+b+c = 193.19+64.41+182.14 = 439.74 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 439.74 }{ 2 } = 219.87 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 219.87 * (219.87-193.19)(219.87-64.41)(219.87-182.14) } ; ; T = sqrt{ 34407602.33 } = 5865.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5865.8 }{ 193.19 } = 60.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5865.8 }{ 64.41 } = 182.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5865.8 }{ 182.14 } = 64.41 ; ;

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{ 64.41**2+182.14**2-193.19**2 }{ 2 * 64.41 * 182.14 } ) = 90° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 193.19**2+182.14**2-64.41**2 }{ 2 * 193.19 * 182.14 } ) = 19° 28'30" ; ; gamma = 180° - alpha - beta = 180° - 90° - 19° 28'30" = 70° 31'29" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5865.8 }{ 219.87 } = 26.68 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 193.19 }{ 2 * sin 90° } = 96.6 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 64.41**2+2 * 182.14**2 - 193.19**2 } }{ 2 } = 96.596 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 182.14**2+2 * 193.19**2 - 64.41**2 } }{ 2 } = 184.965 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 64.41**2+2 * 193.19**2 - 182.14**2 } }{ 2 } = 111.545 ; ;
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