14 16 25 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 16   c = 25

Area: T = 103.3122329855
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 31.10218950348° = 31°6'7″ = 0.5432830472 rad
Angle ∠ B = β = 36.18222872212° = 36°10'56″ = 0.63215000429 rad
Angle ∠ C = γ = 112.7165817744° = 112°42'57″ = 1.96772621387 rad

Height: ha = 14.7598904265
Height: hb = 12.91440412318
Height: hc = 8.26549863884

Median: ma = 19.78663589374
Median: mb = 18.6154510469
Median: mc = 8.35216465442

Inradius: r = 3.75768119947
Circumradius: R = 13.55111414946

Vertex coordinates: A[25; 0] B[0; 0] C[11.3; 8.26549863884]
Centroid: CG[12.1; 2.75549954628]
Coordinates of the circumscribed circle: U[12.5; -5.2332918479]
Coordinates of the inscribed circle: I[11.5; 3.75768119947]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.8988104965° = 148°53'53″ = 0.5432830472 rad
∠ B' = β' = 143.8187712779° = 143°49'4″ = 0.63215000429 rad
∠ C' = γ' = 67.2844182256° = 67°17'3″ = 1.96772621387 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 = 14 ; ; b = 16 ; ; c = 25 ; ;

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

p = a+b+c = 14+16+25 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-14)(27.5-16)(27.5-25) } ; ; T = sqrt{ 10673.44 } = 103.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 103.31 }{ 14 } = 14.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 103.31 }{ 16 } = 12.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 103.31 }{ 25 } = 8.26 ; ;

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{ 14**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 31° 6'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 36° 10'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-16**2 }{ 2 * 16 * 14 } ) = 112° 42'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 103.31 }{ 27.5 } = 3.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 31° 6'7" } = 13.55 ; ;




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