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?

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

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

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

2. Semiperimeter of the triangle

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

3. 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 ; ;

4. 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 ; ;

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

6. Inradius

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

7. Circumradius

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




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