6 23 25 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 23   c = 25

Area: T = 67.35498329619
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 13.54880233388° = 13°32'53″ = 0.23664576144 rad
Angle ∠ B = β = 63.89661188627° = 63°53'46″ = 1.11551976534 rad
Angle ∠ C = γ = 102.5565857799° = 102°33'21″ = 1.79899373858 rad

Height: ha = 22.45499443206
Height: hb = 5.85765072141
Height: hc = 5.3887986637

Median: ma = 23.83327505756
Median: mb = 14.08801278403
Median: mc = 11.23661025271

Inradius: r = 2.49444382578
Circumradius: R = 12.80662678416

Vertex coordinates: A[25; 0] B[0; 0] C[2.64; 5.3887986637]
Centroid: CG[9.21333333333; 1.79659955457]
Coordinates of the circumscribed circle: U[12.5; -2.78439712699]
Coordinates of the inscribed circle: I[4; 2.49444382578]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.4521976661° = 166°27'7″ = 0.23664576144 rad
∠ B' = β' = 116.1043881137° = 116°6'14″ = 1.11551976534 rad
∠ C' = γ' = 77.44441422014° = 77°26'39″ = 1.79899373858 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 = 6 ; ; b = 23 ; ; c = 25 ; ;

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

p = a+b+c = 6+23+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 * (27-6)(27-23)(27-25) } ; ; T = sqrt{ 4536 } = 67.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.35 }{ 6 } = 22.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.35 }{ 23 } = 5.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.35 }{ 25 } = 5.39 ; ;

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{ 6**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 13° 32'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-6**2-25**2 }{ 2 * 6 * 25 } ) = 63° 53'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-6**2-23**2 }{ 2 * 23 * 6 } ) = 102° 33'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.35 }{ 27 } = 2.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 13° 32'53" } = 12.81 ; ;




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