38.3 33.1 55.52 triangle

Obtuse scalene triangle.

Sides: a = 38.3   b = 33.1   c = 55.52

Area: T = 620.3922425945
Perimeter: p = 126.92
Semiperimeter: s = 63.46

Angle ∠ A = α = 42.46880648652° = 42°28'5″ = 0.74112075588 rad
Angle ∠ B = β = 35.69877930235° = 35°41'52″ = 0.6233044024 rad
Angle ∠ C = γ = 101.8344142111° = 101°50'3″ = 1.77773410708 rad

Height: ha = 32.39664713287
Height: hb = 37.4865947187
Height: hc = 22.34884303294

Median: ma = 41.50108156546
Median: mb = 44.73300536552
Median: mc = 22.59771768148

Inradius: r = 9.77661176481
Circumradius: R = 28.36328420724

Vertex coordinates: A[55.52; 0] B[0; 0] C[31.10436599424; 22.34884303294]
Centroid: CG[28.87545533141; 7.44994767765]
Coordinates of the circumscribed circle: U[27.76; -5.81766322236]
Coordinates of the inscribed circle: I[30.36; 9.77661176481]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.5321935135° = 137°31'55″ = 0.74112075588 rad
∠ B' = β' = 144.3022206977° = 144°18'8″ = 0.6233044024 rad
∠ C' = γ' = 78.16658578887° = 78°9'57″ = 1.77773410708 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 = 38.3 ; ; b = 33.1 ; ; c = 55.52 ; ;

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

p = a+b+c = 38.3+33.1+55.52 = 126.92 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 126.92 }{ 2 } = 63.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 63.46 * (63.46-38.3)(63.46-33.1)(63.46-55.52) } ; ; T = sqrt{ 384886.76 } = 620.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 620.39 }{ 38.3 } = 32.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 620.39 }{ 33.1 } = 37.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 620.39 }{ 55.52 } = 22.35 ; ;

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{ 33.1**2+55.52**2-38.3**2 }{ 2 * 33.1 * 55.52 } ) = 42° 28'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38.3**2+55.52**2-33.1**2 }{ 2 * 38.3 * 55.52 } ) = 35° 41'52" ; ;
 gamma = 180° - alpha - beta = 180° - 42° 28'5" - 35° 41'52" = 101° 50'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 620.39 }{ 63.46 } = 9.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 38.3 }{ 2 * sin 42° 28'5" } = 28.36 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.1**2+2 * 55.52**2 - 38.3**2 } }{ 2 } = 41.501 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 55.52**2+2 * 38.3**2 - 33.1**2 } }{ 2 } = 44.73 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.1**2+2 * 38.3**2 - 55.52**2 } }{ 2 } = 22.597 ; ;
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