10 19 25 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 19   c = 25

Area: T = 85.69771411425
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 21.15111820865° = 21°9'4″ = 0.36991577681 rad
Angle ∠ B = β = 43.28110120024° = 43°16'52″ = 0.7555396163 rad
Angle ∠ C = γ = 115.5687805911° = 115°34'4″ = 2.01770387225 rad

Height: ha = 17.13994282285
Height: hb = 9.02107516992
Height: hc = 6.85657712914

Median: ma = 21.63333076528
Median: mb = 16.5
Median: mc = 8.61768439698

Inradius: r = 3.17439681905
Circumradius: R = 13.85769383315

Vertex coordinates: A[25; 0] B[0; 0] C[7.28; 6.85657712914]
Centroid: CG[10.76; 2.28552570971]
Coordinates of the circumscribed circle: U[12.5; -5.98803628589]
Coordinates of the inscribed circle: I[8; 3.17439681905]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.8498817913° = 158°50'56″ = 0.36991577681 rad
∠ B' = β' = 136.7198987998° = 136°43'8″ = 0.7555396163 rad
∠ C' = γ' = 64.4322194089° = 64°25'56″ = 2.01770387225 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 = 19 ; ; c = 25 ; ;

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

p = a+b+c = 10+19+25 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-10)(27-19)(27-25) } ; ; T = sqrt{ 7344 } = 85.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 85.7 }{ 10 } = 17.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 85.7 }{ 19 } = 9.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 85.7 }{ 25 } = 6.86 ; ;

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**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 21° 9'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-10**2-25**2 }{ 2 * 10 * 25 } ) = 43° 16'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-10**2-19**2 }{ 2 * 19 * 10 } ) = 115° 34'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 85.7 }{ 27 } = 3.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 21° 9'4" } = 13.86 ; ;




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