19 25 30 triangle

Acute scalene triangle.

Sides: a = 19   b = 25   c = 30

Area: T = 236.5254840133
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 39.10442158089° = 39°6'15″ = 0.68224973173 rad
Angle ∠ B = β = 56.09896705572° = 56°5'23″ = 0.97989494276 rad
Angle ∠ C = γ = 84.80661136338° = 84°48'22″ = 1.48801459087 rad

Height: ha = 24.8977351593
Height: hb = 18.92219872106
Height: hc = 15.76883226755

Median: ma = 25.92877843249
Median: mb = 21.77772817404
Median: mc = 16.37107055437

Inradius: r = 6.39325632468
Circumradius: R = 15.06218429675

Vertex coordinates: A[30; 0] B[0; 0] C[10.6; 15.76883226755]
Centroid: CG[13.53333333333; 5.25661075585]
Coordinates of the circumscribed circle: U[15; 1.36334931528]
Coordinates of the inscribed circle: I[12; 6.39325632468]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.8965784191° = 140°53'45″ = 0.68224973173 rad
∠ B' = β' = 123.9110329443° = 123°54'37″ = 0.97989494276 rad
∠ C' = γ' = 95.19438863662° = 95°11'38″ = 1.48801459087 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 = 19 ; ; b = 25 ; ; c = 30 ; ;

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

p = a+b+c = 19+25+30 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-19)(37-25)(37-30) } ; ; T = sqrt{ 55944 } = 236.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 236.52 }{ 19 } = 24.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 236.52 }{ 25 } = 18.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 236.52 }{ 30 } = 15.77 ; ;

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{ 19**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 39° 6'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 56° 5'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-19**2-25**2 }{ 2 * 25 * 19 } ) = 84° 48'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 236.52 }{ 37 } = 6.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 39° 6'15" } = 15.06 ; ;




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