16 17 25 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 17   c = 25

Area: T = 134.5211373766
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 39.27548962352° = 39°16'30″ = 0.68554762527 rad
Angle ∠ B = β = 42.26985844296° = 42°16'7″ = 0.73877259685 rad
Angle ∠ C = γ = 98.45765193353° = 98°27'23″ = 1.71883904325 rad

Height: ha = 16.81551717208
Height: hb = 15.82660439725
Height: hc = 10.76217099013

Median: ma = 19.82442276016
Median: mb = 19.19898410624
Median: mc = 10.78219293264

Inradius: r = 4.63986680609
Circumradius: R = 12.63773969608

Vertex coordinates: A[25; 0] B[0; 0] C[11.84; 10.76217099013]
Centroid: CG[12.28; 3.58772366338]
Coordinates of the circumscribed circle: U[12.5; -1.85884407295]
Coordinates of the inscribed circle: I[12; 4.63986680609]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.7255103765° = 140°43'30″ = 0.68554762527 rad
∠ B' = β' = 137.731141557° = 137°43'53″ = 0.73877259685 rad
∠ C' = γ' = 81.54334806647° = 81°32'37″ = 1.71883904325 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 = 16 ; ; b = 17 ; ; c = 25 ; ;

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

p = a+b+c = 16+17+25 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-16)(29-17)(29-25) } ; ; T = sqrt{ 18096 } = 134.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 134.52 }{ 16 } = 16.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 134.52 }{ 17 } = 15.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 134.52 }{ 25 } = 10.76 ; ;

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{ 16**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 39° 16'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 42° 16'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 98° 27'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 134.52 }{ 29 } = 4.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 39° 16'30" } = 12.64 ; ;




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