4.24 5.1 2.83 triangle

Obtuse scalene triangle.

Sides: a = 4.24   b = 5.1   c = 2.83

Area: T = 65.9995971235
Perimeter: p = 12.17
Semiperimeter: s = 6.085

Angle ∠ A = α = 56.24399501064° = 56°14'24″ = 0.98215723005 rad
Angle ∠ B = β = 90.05661058668° = 90°3'22″ = 1.57217755589 rad
Angle ∠ C = γ = 33.70439440268° = 33°42'14″ = 0.58882447942 rad

Height: ha = 2.83299986432
Height: hb = 2.35327831857
Height: hc = 4.24399979671

Median: ma = 3.53876616571
Median: mb = 2.54876950367
Median: mc = 4.47111939121

Inradius: r = 0.98659650162
Circumradius: R = 2.55500012226

Vertex coordinates: A[2.83; 0] B[0; 0] C[-0.00441519435; 4.24399979671]
Centroid: CG[0.94219493522; 1.41333326557]
Coordinates of the circumscribed circle: U[1.415; 2.12113866303]
Coordinates of the inscribed circle: I[0.985; 0.98659650162]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.7660049894° = 123°45'36″ = 0.98215723005 rad
∠ B' = β' = 89.94438941332° = 89°56'38″ = 1.57217755589 rad
∠ C' = γ' = 146.2966055973° = 146°17'46″ = 0.58882447942 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 = 4.24 ; ; b = 5.1 ; ; c = 2.83 ; ;

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

p = a+b+c = 4.24+5.1+2.83 = 12.17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.17 }{ 2 } = 6.09 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.09 * (6.09-4.24)(6.09-5.1)(6.09-2.83) } ; ; T = sqrt{ 36 } = 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 * 6 }{ 4.24 } = 2.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6 }{ 5.1 } = 2.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6 }{ 2.83 } = 4.24 ; ;

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{ 5.1**2+2.83**2-4.24**2 }{ 2 * 5.1 * 2.83 } ) = 56° 14'24" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.24**2+2.83**2-5.1**2 }{ 2 * 4.24 * 2.83 } ) = 90° 3'22" ; ;
 gamma = 180° - alpha - beta = 180° - 56° 14'24" - 90° 3'22" = 33° 42'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6 }{ 6.09 } = 0.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.24 }{ 2 * sin 56° 14'24" } = 2.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 2.83**2 - 4.24**2 } }{ 2 } = 3.538 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.83**2+2 * 4.24**2 - 5.1**2 } }{ 2 } = 2.548 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 4.24**2 - 2.83**2 } }{ 2 } = 4.471 ; ;
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