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 = 26.83328   b = 33.94111   c = 36

Area: T = 4321.999572611
Perimeter: p = 96.77439
Semiperimeter: s = 48.387695

Angle ∠ A = α = 454.999986357° = 45° = 0.78553979253 rad
Angle ∠ B = β = 63.43549026306° = 63°26'6″ = 1.10771479116 rad
Angle ∠ C = γ = 71.56551110124° = 71°33'54″ = 1.24990468167 rad

Height: ha = 32.19993658963
Height: hb = 25.45658380613
Height: hc = 243.9999762562

Median: ma = 32.31109787169
Median: mb = 26.83328159278
Median: mc = 24.73986077321

Inradius: r = 8.92880182489
Circumradius: R = 18.97436593561

Vertex coordinates: A[36; 0] B[0; 0] C[122.0000123143; 243.9999762562]
Centroid: CG[166.0000041048; 87.9999920854]
Coordinates of the circumscribed circle: U[18; 65.9999791135]
Coordinates of the inscribed circle: I[14.446585; 8.92880182489]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1355.000013643° = 135° = 0.78553979253 rad
∠ B' = β' = 116.5655097369° = 116°33'54″ = 1.10771479116 rad
∠ C' = γ' = 108.4354888988° = 108°26'6″ = 1.24990468167 rad

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How did we calculate this triangle?

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

a = 26.833 ; ; b = 33.941 ; ; c = 36 ; ;


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 = 26.83 ; ; b = 33.94 ; ; c = 36 ; ;

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

p = a+b+c = 26.83+33.94+36 = 96.77 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 96.77 }{ 2 } = 48.39 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 48.39 * (48.39-26.83)(48.39-33.94)(48.39-36) } ; ; T = sqrt{ 186623.63 } = 432 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 432 }{ 26.83 } = 32.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 432 }{ 33.94 } = 25.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 432 }{ 36 } = 24 ; ;

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{ 33.94**2+36**2-26.83**2 }{ 2 * 33.94 * 36 } ) = 45° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 26.83**2+36**2-33.94**2 }{ 2 * 26.83 * 36 } ) = 63° 26'6" ; ; gamma = 180° - alpha - beta = 180° - 45° - 63° 26'6" = 71° 33'54" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 432 }{ 48.39 } = 8.93 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 26.83 }{ 2 * sin 45° } = 18.97 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.94**2+2 * 36**2 - 26.83**2 } }{ 2 } = 32.311 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 36**2+2 * 26.83**2 - 33.94**2 } }{ 2 } = 26.833 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.94**2+2 * 26.83**2 - 36**2 } }{ 2 } = 24.739 ; ;
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