18.2 17.1 12.3 triangle

Acute scalene triangle.

Sides: a = 18.2   b = 17.1   c = 12.3

Area: T = 101.3377179752
Perimeter: p = 47.6
Semiperimeter: s = 23.8

Angle ∠ A = α = 74.49438507276° = 74°29'38″ = 1.33001629677 rad
Angle ∠ B = β = 64.87220959542° = 64°52'20″ = 1.13222316671 rad
Angle ∠ C = γ = 40.63440533182° = 40°38'3″ = 0.70991980188 rad

Height: ha = 11.13659538189
Height: hb = 11.85223017253
Height: hc = 16.47875902035

Median: ma = 11.79215223784
Median: mb = 12.96877484553
Median: mc = 16.55330208723

Inradius: r = 4.25878646954
Circumradius: R = 9.4443735284

Vertex coordinates: A[12.3; 0] B[0; 0] C[7.72884552846; 16.47875902035]
Centroid: CG[6.67661517615; 5.49325300678]
Coordinates of the circumscribed circle: U[6.15; 7.16767032947]
Coordinates of the inscribed circle: I[6.7; 4.25878646954]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.5066149272° = 105°30'22″ = 1.33001629677 rad
∠ B' = β' = 115.1287904046° = 115°7'40″ = 1.13222316671 rad
∠ C' = γ' = 139.3665946682° = 139°21'57″ = 0.70991980188 rad

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How did we calculate this triangle?

a = 18.2 ; ; b = 17.1 ; ; c = 12.3 ; ;

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

p = a+b+c = 18.2+17.1+12.3 = 47.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47.6 }{ 2 } = 23.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.8 * (23.8-18.2)(23.8-17.1)(23.8-12.3) } ; ; T = sqrt{ 10269.22 } = 101.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.34 }{ 18.2 } = 11.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.34 }{ 17.1 } = 11.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.34 }{ 12.3 } = 16.48 ; ;

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{ 17.1**2+12.3**2-18.2**2 }{ 2 * 17.1 * 12.3 } ) = 74° 29'38" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.2**2+12.3**2-17.1**2 }{ 2 * 18.2 * 12.3 } ) = 64° 52'20" ; ; gamma = 180° - alpha - beta = 180° - 74° 29'38" - 64° 52'20" = 40° 38'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.34 }{ 23.8 } = 4.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18.2 }{ 2 * sin 74° 29'38" } = 9.44 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.1**2+2 * 12.3**2 - 18.2**2 } }{ 2 } = 11.792 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.3**2+2 * 18.2**2 - 17.1**2 } }{ 2 } = 12.968 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.1**2+2 * 18.2**2 - 12.3**2 } }{ 2 } = 16.553 ; ;
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