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 = 105   b = 780   c = 772

Area: T = 40528.50881139
Perimeter: p = 1657
Semiperimeter: s = 828.5

Angle ∠ A = α = 7.7366093525° = 7°44'10″ = 0.13550203033 rad
Angle ∠ B = β = 90.49216074957° = 90°29'30″ = 1.57993764962 rad
Angle ∠ C = γ = 81.77222989793° = 81°46'20″ = 1.42771958541 rad

Height: ha = 771.9721583122
Height: hb = 103.9199251574
Height: hc = 104.996613501

Median: ma = 774.2322361762
Median: mb = 389.1077311676
Median: mc = 400.8954624559

Inradius: r = 48.91879337524
Circumradius: R = 390.0144356205

Vertex coordinates: A[772; 0] B[0; 0] C[-0.90109067358; 104.996613501]
Centroid: CG[257.0333031088; 34.999871167]
Coordinates of the circumscribed circle: U[386; 55.81439592418]
Coordinates of the inscribed circle: I[48.5; 48.91879337524]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.2643906475° = 172°15'50″ = 0.13550203033 rad
∠ B' = β' = 89.50883925043° = 89°30'30″ = 1.57993764962 rad
∠ C' = γ' = 98.22877010207° = 98°13'40″ = 1.42771958541 rad

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How did we calculate this triangle?

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

a = 105 ; ; b = 780 ; ; c = 772 ; ;

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

p = a+b+c = 105+780+772 = 1657 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1657 }{ 2 } = 828.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 828.5 * (828.5-105)(828.5-780)(828.5-772) } ; ; T = sqrt{ 1642559969.94 } = 40528.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40528.51 }{ 105 } = 771.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40528.51 }{ 780 } = 103.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40528.51 }{ 772 } = 105 ; ;

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{ 780**2+772**2-105**2 }{ 2 * 780 * 772 } ) = 7° 44'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 105**2+772**2-780**2 }{ 2 * 105 * 772 } ) = 90° 29'30" ; ;
 gamma = 180° - alpha - beta = 180° - 7° 44'10" - 90° 29'30" = 81° 46'20" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40528.51 }{ 828.5 } = 48.92 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 105 }{ 2 * sin 7° 44'10" } = 390.01 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 780**2+2 * 772**2 - 105**2 } }{ 2 } = 774.232 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 772**2+2 * 105**2 - 780**2 } }{ 2 } = 389.107 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 780**2+2 * 105**2 - 772**2 } }{ 2 } = 400.895 ; ;
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