14 25 30 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 25   c = 30

Area: T = 173.8821964275
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 27.62551660544° = 27°37'31″ = 0.48221501041 rad
Angle ∠ B = β = 55.89547902371° = 55°53'41″ = 0.97655481243 rad
Angle ∠ C = γ = 96.48800437085° = 96°28'48″ = 1.68438944252 rad

Height: ha = 24.84402806107
Height: hb = 13.9110557142
Height: hc = 11.59221309516

Median: ma = 26.71114207784
Median: mb = 19.79326754129
Median: mc = 13.62198384719

Inradius: r = 5.04400569355
Circumradius: R = 15.09664478171

Vertex coordinates: A[30; 0] B[0; 0] C[7.85; 11.59221309516]
Centroid: CG[12.61766666667; 3.86440436505]
Coordinates of the circumscribed circle: U[15; -1.70437419679]
Coordinates of the inscribed circle: I[9.5; 5.04400569355]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.3754833946° = 152°22'29″ = 0.48221501041 rad
∠ B' = β' = 124.1055209763° = 124°6'19″ = 0.97655481243 rad
∠ C' = γ' = 83.52199562915° = 83°31'12″ = 1.68438944252 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 = 25 ; ; c = 30 ; ;

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

p = a+b+c = 14+25+30 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-14)(34.5-25)(34.5-30) } ; ; T = sqrt{ 30234.94 } = 173.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 173.88 }{ 14 } = 24.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 173.88 }{ 25 } = 13.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 173.88 }{ 30 } = 11.59 ; ;

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**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 27° 37'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 55° 53'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-25**2 }{ 2 * 25 * 14 } ) = 96° 28'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 173.88 }{ 34.5 } = 5.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 27° 37'31" } = 15.1 ; ;




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