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 = 128   b = 90   c = 130

Area: T = 5439.00657915
Perimeter: p = 348
Semiperimeter: s = 174

Angle ∠ A = α = 68.39550345954° = 68°23'42″ = 1.19437185457 rad
Angle ∠ B = β = 40.82331687687° = 40°49'23″ = 0.71224987061 rad
Angle ∠ C = γ = 70.78217966359° = 70°46'54″ = 1.23553754018 rad

Height: ha = 84.98444654922
Height: hb = 120.8676795367
Height: hc = 83.6777012177

Median: ma = 91.67333330909
Median: mb = 120.9010785771
Median: mc = 89.53877015564

Inradius: r = 31.25986539742
Circumradius: R = 68.83661098245

Vertex coordinates: A[130; 0] B[0; 0] C[96.86215384615; 83.6777012177]
Centroid: CG[75.62105128205; 27.89223373923]
Coordinates of the circumscribed circle: U[65; 22.65985528172]
Coordinates of the inscribed circle: I[84; 31.25986539742]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.6054965405° = 111°36'18″ = 1.19437185457 rad
∠ B' = β' = 139.1776831231° = 139°10'37″ = 0.71224987061 rad
∠ C' = γ' = 109.2188203364° = 109°13'6″ = 1.23553754018 rad

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How did we calculate this triangle?

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

a = 128 ; ; b = 90 ; ; c = 130 ; ;


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 = 128 ; ; b = 90 ; ; c = 130 ; ; : Nr. 1

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

p = a+b+c = 128+90+130 = 348 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 348 }{ 2 } = 174 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 174 * (174-128)(174-90)(174-130) } ; ; T = sqrt{ 29582784 } = 5439.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5439.01 }{ 128 } = 84.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5439.01 }{ 90 } = 120.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5439.01 }{ 130 } = 83.68 ; ;

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{ 90**2+130**2-128**2 }{ 2 * 90 * 130 } ) = 68° 23'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 128**2+130**2-90**2 }{ 2 * 128 * 130 } ) = 40° 49'23" ; ; gamma = 180° - alpha - beta = 180° - 68° 23'42" - 40° 49'23" = 70° 46'54" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5439.01 }{ 174 } = 31.26 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 128 }{ 2 * sin 68° 23'42" } = 68.84 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 130**2 - 128**2 } }{ 2 } = 91.673 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 130**2+2 * 128**2 - 90**2 } }{ 2 } = 120.901 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 128**2 - 130**2 } }{ 2 } = 89.538 ; ;
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