21.21 36.51 33.73 triangle

Acute scalene triangle.

Sides: a = 21.21   b = 36.51   c = 33.73

Area: T = 351.9988328989
Perimeter: p = 91.45
Semiperimeter: s = 45.725

Angle ∠ A = α = 34.86664884229° = 34°51'59″ = 0.60985350216 rad
Angle ∠ B = β = 79.75503848833° = 79°45'1″ = 1.39219067959 rad
Angle ∠ C = γ = 65.38331266938° = 65°22'59″ = 1.14111508361 rad

Height: ha = 33.19217330494
Height: hb = 19.28222968496
Height: hc = 20.87215285496

Median: ma = 33.50994087534
Median: mb = 21.46602766758
Median: mc = 24.63772456862

Inradius: r = 7.69881591906
Circumradius: R = 18.55110394737

Vertex coordinates: A[33.73; 0] B[0; 0] C[3.77440423955; 20.87215285496]
Centroid: CG[12.50113474652; 6.95771761832]
Coordinates of the circumscribed circle: U[16.865; 7.72774083983]
Coordinates of the inscribed circle: I[9.215; 7.69881591906]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.1343511577° = 145°8'1″ = 0.60985350216 rad
∠ B' = β' = 100.2549615117° = 100°14'59″ = 1.39219067959 rad
∠ C' = γ' = 114.6176873306° = 114°37'1″ = 1.14111508361 rad

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How did we calculate this triangle?

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

p = a+b+c = 21.21+36.51+33.73 = 91.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 91.45 }{ 2 } = 45.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45.73 * (45.73-21.21)(45.73-36.51)(45.73-33.73) } ; ; T = sqrt{ 123902.82 } = 352 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 352 }{ 21.21 } = 33.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 352 }{ 36.51 } = 19.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 352 }{ 33.73 } = 20.87 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 36.51**2+33.73**2-21.21**2 }{ 2 * 36.51 * 33.73 } ) = 34° 51'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 21.21**2+33.73**2-36.51**2 }{ 2 * 21.21 * 33.73 } ) = 79° 45'1" ; ;
 gamma = 180° - alpha - beta = 180° - 34° 51'59" - 79° 45'1" = 65° 22'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 352 }{ 45.73 } = 7.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 21.21 }{ 2 * sin 34° 51'59" } = 18.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.51**2+2 * 33.73**2 - 21.21**2 } }{ 2 } = 33.509 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.73**2+2 * 21.21**2 - 36.51**2 } }{ 2 } = 21.46 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.51**2+2 * 21.21**2 - 33.73**2 } }{ 2 } = 24.637 ; ;
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