58 83 31 triangle

Obtuse scalene triangle.

Sides: a = 58   b = 83   c = 31

Area: T = 630.3333245197
Perimeter: p = 172
Semiperimeter: s = 86

Angle ∠ A = α = 29.33879374642° = 29°20'17″ = 0.51220436045 rad
Angle ∠ B = β = 135.4810712428° = 135°28'51″ = 2.36545845048 rad
Angle ∠ C = γ = 15.18113501079° = 15°10'53″ = 0.26549645443 rad

Height: ha = 21.73656291447
Height: hb = 15.18987528963
Height: hc = 40.66766609804

Median: ma = 55.53437735077
Median: mb = 20.98221352584
Median: mc = 69.90217167171

Inradius: r = 7.32994563395
Circumradius: R = 59.18985328662

Vertex coordinates: A[31; 0] B[0; 0] C[-41.35548387097; 40.66766609804]
Centroid: CG[-3.45216129032; 13.55655536601]
Coordinates of the circumscribed circle: U[15.5; 57.12329588069]
Coordinates of the inscribed circle: I[3; 7.32994563395]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.6622062536° = 150°39'43″ = 0.51220436045 rad
∠ B' = β' = 44.51992875721° = 44°31'9″ = 2.36545845048 rad
∠ C' = γ' = 164.8198649892° = 164°49'7″ = 0.26549645443 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 = 58+83+31 = 172 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 172 }{ 2 } = 86 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 86 * (86-58)(86-83)(86-31) } ; ; T = sqrt{ 397320 } = 630.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 630.33 }{ 58 } = 21.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 630.33 }{ 83 } = 15.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 630.33 }{ 31 } = 40.67 ; ;

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{ 83**2+31**2-58**2 }{ 2 * 83 * 31 } ) = 29° 20'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 58**2+31**2-83**2 }{ 2 * 58 * 31 } ) = 135° 28'51" ; ; gamma = 180° - alpha - beta = 180° - 29° 20'17" - 135° 28'51" = 15° 10'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 630.33 }{ 86 } = 7.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 58 }{ 2 * sin 29° 20'17" } = 59.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 83**2+2 * 31**2 - 58**2 } }{ 2 } = 55.534 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 31**2+2 * 58**2 - 83**2 } }{ 2 } = 20.982 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 83**2+2 * 58**2 - 31**2 } }{ 2 } = 69.902 ; ;
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