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 = 4.65   b = 3.36   c = 5.78

Area: T = 7.811101462
Perimeter: p = 13.79
Semiperimeter: s = 6.895

Angle ∠ A = α = 53.55220404687° = 53°33'7″ = 0.93546594273 rad
Angle ∠ B = β = 35.53879143752° = 35°32'16″ = 0.62202536151 rad
Angle ∠ C = γ = 90.9110045156° = 90°54'36″ = 1.58766796111 rad

Height: ha = 3.36595761807
Height: hb = 4.64994134643
Height: hc = 2.70327732249

Median: ma = 4.11662331081
Median: mb = 4.96992101988
Median: mc = 2.84767437538

Inradius: r = 1.13328520116
Circumradius: R = 2.89903645811

Vertex coordinates: A[5.78; 0] B[0; 0] C[3.7843849481; 2.70327732249]
Centroid: CG[3.1887949827; 0.90109244083]
Coordinates of the circumscribed circle: U[2.89; -0.04659065522]
Coordinates of the inscribed circle: I[3.535; 1.13328520116]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.4487959531° = 126°26'53″ = 0.93546594273 rad
∠ B' = β' = 144.4622085625° = 144°27'44″ = 0.62202536151 rad
∠ C' = γ' = 89.0989954844° = 89°5'24″ = 1.58766796111 rad

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How did we calculate this triangle?

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

a = 4.65 ; ; b = 3.36 ; ; c = 5.78 ; ;

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

p = a+b+c = 4.65+3.36+5.78 = 13.79 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.79 }{ 2 } = 6.9 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.9 * (6.9-4.65)(6.9-3.36)(6.9-5.78) } ; ; T = sqrt{ 61.01 } = 7.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.81 }{ 4.65 } = 3.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.81 }{ 3.36 } = 4.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.81 }{ 5.78 } = 2.7 ; ;

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{ 3.36**2+5.78**2-4.65**2 }{ 2 * 3.36 * 5.78 } ) = 53° 33'7" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.65**2+5.78**2-3.36**2 }{ 2 * 4.65 * 5.78 } ) = 35° 32'16" ; ; gamma = 180° - alpha - beta = 180° - 53° 33'7" - 35° 32'16" = 90° 54'36" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.81 }{ 6.9 } = 1.13 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.65 }{ 2 * sin 53° 33'7" } = 2.89 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.36**2+2 * 5.78**2 - 4.65**2 } }{ 2 } = 4.116 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.78**2+2 * 4.65**2 - 3.36**2 } }{ 2 } = 4.969 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.36**2+2 * 4.65**2 - 5.78**2 } }{ 2 } = 2.847 ; ;
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