5.96 51.08 47.3 triangle

Obtuse scalene triangle.

Sides: a = 5.96   b = 51.08   c = 47.3

Area: T = 113.1244359217
Perimeter: p = 104.34
Semiperimeter: s = 52.17

Angle ∠ A = α = 5.37332061148° = 5°22'24″ = 0.09437801381 rad
Angle ∠ B = β = 126.625451958° = 126°37'28″ = 2.21100147804 rad
Angle ∠ C = γ = 48.00222743052° = 48°8″ = 0.83877977351 rad

Height: ha = 37.96111943682
Height: hb = 4.42993014572
Height: hc = 4.78332710028

Median: ma = 49.13660132693
Median: mb = 22.00325953015
Median: mc = 27.62328438073

Inradius: r = 2.16883795135
Circumradius: R = 31.82330766999

Vertex coordinates: A[47.3; 0] B[0; 0] C[-3.55655475687; 4.78332710028]
Centroid: CG[14.58114841438; 1.59444236676]
Coordinates of the circumscribed circle: U[23.65; 21.29328558594]
Coordinates of the inscribed circle: I[1.09; 2.16883795135]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.6276793885° = 174°37'36″ = 0.09437801381 rad
∠ B' = β' = 53.375548042° = 53°22'32″ = 2.21100147804 rad
∠ C' = γ' = 131.9987725695° = 131°59'52″ = 0.83877977351 rad

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How did we calculate this triangle?

a = 5.96 ; ; b = 51.08 ; ; c = 47.3 ; ;

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

p = a+b+c = 5.96+51.08+47.3 = 104.34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 104.34 }{ 2 } = 52.17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52.17 * (52.17-5.96)(52.17-51.08)(52.17-47.3) } ; ; T = sqrt{ 12797.12 } = 113.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 113.12 }{ 5.96 } = 37.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 113.12 }{ 51.08 } = 4.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 113.12 }{ 47.3 } = 4.78 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 5.96**2-51.08**2-47.3**2 }{ 2 * 51.08 * 47.3 } ) = 5° 22'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 51.08**2-5.96**2-47.3**2 }{ 2 * 5.96 * 47.3 } ) = 126° 37'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 47.3**2-5.96**2-51.08**2 }{ 2 * 51.08 * 5.96 } ) = 48° 8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 113.12 }{ 52.17 } = 2.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.96 }{ 2 * sin 5° 22'24" } = 31.82 ; ;




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