10 28 30 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 28   c = 30

Area: T = 139.9432845476
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 19.46329509463° = 19°27'47″ = 0.34396925762 rad
Angle ∠ B = β = 68.98998039759° = 68°53'59″ = 1.20325284334 rad
Angle ∠ C = γ = 91.63772450778° = 91°38'14″ = 1.59993716441 rad

Height: ha = 27.98985690953
Height: hb = 9.9965917534
Height: hc = 9.33295230318

Median: ma = 28.58332118559
Median: mb = 17.43655957742
Median: mc = 14.73109198627

Inradius: r = 4.11659660434
Circumradius: R = 15.00661262

Vertex coordinates: A[30; 0] B[0; 0] C[3.6; 9.33295230318]
Centroid: CG[11.2; 3.11098410106]
Coordinates of the circumscribed circle: U[15; -0.42987464629]
Coordinates of the inscribed circle: I[6; 4.11659660434]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.5377049054° = 160°32'13″ = 0.34396925762 rad
∠ B' = β' = 111.1100196024° = 111°6'1″ = 1.20325284334 rad
∠ C' = γ' = 88.36327549222° = 88°21'46″ = 1.59993716441 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 = 10 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 10+28+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-10)(34-28)(34-30) } ; ; T = sqrt{ 19584 } = 139.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.94 }{ 10 } = 27.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.94 }{ 28 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.94 }{ 30 } = 9.33 ; ;

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{ 10**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 19° 27'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-10**2-30**2 }{ 2 * 10 * 30 } ) = 68° 53'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-10**2-28**2 }{ 2 * 28 * 10 } ) = 91° 38'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.94 }{ 34 } = 4.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 19° 27'47" } = 15.01 ; ;




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