37.9 26.4 40.59 triangle

Acute scalene triangle.

Sides: a = 37.9   b = 26.4   c = 40.59

Area: T = 485.3132936148
Perimeter: p = 104.89
Semiperimeter: s = 52.445

Angle ∠ A = α = 64.93302783567° = 64°55'49″ = 1.13332471416 rad
Angle ∠ B = β = 39.12201025903° = 39°7'12″ = 0.68327745939 rad
Angle ∠ C = γ = 75.9549619053° = 75°56'59″ = 1.32655709181 rad

Height: ha = 25.61101813271
Height: hb = 36.76661315264
Height: hc = 23.91329310741

Median: ma = 28.51658122802
Median: mb = 36.98329562096
Median: mc = 25.58990205948

Inradius: r = 9.25437503317
Circumradius: R = 20.92108983395

Vertex coordinates: A[40.59; 0] B[0; 0] C[29.40437706332; 23.91329310741]
Centroid: CG[23.33112568777; 7.97109770247]
Coordinates of the circumscribed circle: U[20.295; 5.07990710107]
Coordinates of the inscribed circle: I[26.045; 9.25437503317]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.0769721643° = 115°4'11″ = 1.13332471416 rad
∠ B' = β' = 140.887989741° = 140°52'48″ = 0.68327745939 rad
∠ C' = γ' = 104.0550380947° = 104°3'1″ = 1.32655709181 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 = 37.9 ; ; b = 26.4 ; ; c = 40.59 ; ;

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

p = a+b+c = 37.9+26.4+40.59 = 104.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 104.89 }{ 2 } = 52.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52.45 * (52.45-37.9)(52.45-26.4)(52.45-40.59) } ; ; T = sqrt{ 235528.65 } = 485.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 485.31 }{ 37.9 } = 25.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 485.31 }{ 26.4 } = 36.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 485.31 }{ 40.59 } = 23.91 ; ;

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{ 26.4**2+40.59**2-37.9**2 }{ 2 * 26.4 * 40.59 } ) = 64° 55'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37.9**2+40.59**2-26.4**2 }{ 2 * 37.9 * 40.59 } ) = 39° 7'12" ; ;
 gamma = 180° - alpha - beta = 180° - 64° 55'49" - 39° 7'12" = 75° 56'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 485.31 }{ 52.45 } = 9.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37.9 }{ 2 * sin 64° 55'49" } = 20.92 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26.4**2+2 * 40.59**2 - 37.9**2 } }{ 2 } = 28.516 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 40.59**2+2 * 37.9**2 - 26.4**2 } }{ 2 } = 36.983 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26.4**2+2 * 37.9**2 - 40.59**2 } }{ 2 } = 25.589 ; ;
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