39.1 27.5 47.59 triangle

Acute scalene triangle.

Sides: a = 39.1   b = 27.5   c = 47.59

Area: T = 537.6011159699
Perimeter: p = 114.19
Semiperimeter: s = 57.095

Angle ∠ A = α = 55.2421738751° = 55°14'30″ = 0.96441502257 rad
Angle ∠ B = β = 35.29878406718° = 35°17'52″ = 0.61660635386 rad
Angle ∠ C = γ = 89.46604205772° = 89°27'38″ = 1.56113788893 rad

Height: ha = 27.49987805472
Height: hb = 39.09882661599
Height: hc = 22.59330304559

Median: ma = 33.59105723381
Median: mb = 41.32548901995
Median: mc = 24.00768318401

Inradius: r = 9.41659061161
Circumradius: R = 23.7966055206

Vertex coordinates: A[47.59; 0] B[0; 0] C[31.91218312671; 22.59330304559]
Centroid: CG[26.50106104224; 7.5311010152]
Coordinates of the circumscribed circle: U[23.795; 0.22440945503]
Coordinates of the inscribed circle: I[29.595; 9.41659061161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.7588261249° = 124°45'30″ = 0.96441502257 rad
∠ B' = β' = 144.7022159328° = 144°42'8″ = 0.61660635386 rad
∠ C' = γ' = 90.54395794228° = 90°32'22″ = 1.56113788893 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 = 39.1+27.5+47.59 = 114.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 114.19 }{ 2 } = 57.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 57.1 * (57.1-39.1)(57.1-27.5)(57.1-47.59) } ; ; T = sqrt{ 289015.01 } = 537.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 537.6 }{ 39.1 } = 27.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 537.6 }{ 27.5 } = 39.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 537.6 }{ 47.59 } = 22.59 ; ;

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{ 27.5**2+47.59**2-39.1**2 }{ 2 * 27.5 * 47.59 } ) = 55° 14'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 39.1**2+47.59**2-27.5**2 }{ 2 * 39.1 * 47.59 } ) = 35° 17'52" ; ;
 gamma = 180° - alpha - beta = 180° - 55° 14'30" - 35° 17'52" = 89° 27'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 537.6 }{ 57.1 } = 9.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 39.1 }{ 2 * sin 55° 14'30" } = 23.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.5**2+2 * 47.59**2 - 39.1**2 } }{ 2 } = 33.591 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 47.59**2+2 * 39.1**2 - 27.5**2 } }{ 2 } = 41.325 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.5**2+2 * 39.1**2 - 47.59**2 } }{ 2 } = 24.007 ; ;
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