Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 109.3   b = 73.9   c = 95.1

Area: T = 3455.233020394
Perimeter: p = 278.3
Semiperimeter: s = 139.15

Angle ∠ A = α = 79.51113278253° = 79°30'41″ = 1.38877344632 rad
Angle ∠ B = β = 41.66987793931° = 41°40'8″ = 0.72772573957 rad
Angle ∠ C = γ = 58.82198927816° = 58°49'12″ = 1.02766007947 rad

Height: ha = 63.2254706385
Height: hb = 93.51109662771
Height: hc = 72.6655198821

Median: ma = 65.31545274805
Median: mb = 95.5510758762
Median: mc = 80.26773501494

Inradius: r = 24.83109752349
Circumradius: R = 55.57986685446

Vertex coordinates: A[95.1; 0] B[0; 0] C[81.64771608833; 72.6655198821]
Centroid: CG[58.91657202944; 24.22217329403]
Coordinates of the circumscribed circle: U[47.55; 28.77547440855]
Coordinates of the inscribed circle: I[65.25; 24.83109752349]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.4898672175° = 100°29'19″ = 1.38877344632 rad
∠ B' = β' = 138.3311220607° = 138°19'52″ = 0.72772573957 rad
∠ C' = γ' = 121.1880107218° = 121°10'48″ = 1.02766007947 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 = 109.3 ; ; b = 73.9 ; ; c = 95.1 ; ;

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

p = a+b+c = 109.3+73.9+95.1 = 278.3 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 278.3 }{ 2 } = 139.15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 139.15 * (139.15-109.3)(139.15-73.9)(139.15-95.1) } ; ; T = sqrt{ 11938615.76 } = 3455.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3455.23 }{ 109.3 } = 63.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3455.23 }{ 73.9 } = 93.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3455.23 }{ 95.1 } = 72.67 ; ;

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{ 109.3**2-73.9**2-95.1**2 }{ 2 * 73.9 * 95.1 } ) = 79° 30'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 73.9**2-109.3**2-95.1**2 }{ 2 * 109.3 * 95.1 } ) = 41° 40'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 95.1**2-109.3**2-73.9**2 }{ 2 * 73.9 * 109.3 } ) = 58° 49'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3455.23 }{ 139.15 } = 24.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 109.3 }{ 2 * sin 79° 30'41" } = 55.58 ; ;




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