5 14 15 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 14   c = 15

Area: T = 34.98657113691
Perimeter: p = 34
Semiperimeter: s = 17

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 = 13.99442845476
Height: hb = 4.9987958767
Height: hc = 4.66547615159

Median: ma = 14.2921605928
Median: mb = 8.71877978871
Median: mc = 7.36554599313

Inradius: r = 2.05879830217
Circumradius: R = 7.50330631

Vertex coordinates: A[15; 0] B[0; 0] C[1.8; 4.66547615159]
Centroid: CG[5.6; 1.55549205053]
Coordinates of the circumscribed circle: U[7.5; -0.21443732314]
Coordinates of the inscribed circle: I[3; 2.05879830217]

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 = 5 ; ; b = 14 ; ; c = 15 ; ;

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

p = a+b+c = 5+14+15 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-5)(17-14)(17-15) } ; ; T = sqrt{ 1224 } = 34.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.99 }{ 5 } = 13.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.99 }{ 14 } = 5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.99 }{ 15 } = 4.66 ; ;

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**2-14**2-15**2 }{ 2 * 14 * 15 } ) = 19° 27'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-5**2-15**2 }{ 2 * 5 * 15 } ) = 68° 53'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-5**2-14**2 }{ 2 * 14 * 5 } ) = 91° 38'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.99 }{ 17 } = 2.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 19° 27'47" } = 7.5 ; ;




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