19 20 25 triangle

Acute scalene triangle.

Sides: a = 19   b = 20   c = 25

Area: T = 186.9333143129
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 48.39443462161° = 48°23'40″ = 0.84546406808 rad
Angle ∠ B = β = 51.9144106787° = 51°54'51″ = 0.90660720917 rad
Angle ∠ C = γ = 79.69215469969° = 79°41'30″ = 1.39108798811 rad

Height: ha = 19.67771729609
Height: hb = 18.69333143129
Height: hc = 14.95546514503

Median: ma = 20.5498722588
Median: mb = 19.82442276016
Median: mc = 14.97549791319

Inradius: r = 5.84216607228
Circumradius: R = 12.70550771214

Vertex coordinates: A[25; 0] B[0; 0] C[11.72; 14.95546514503]
Centroid: CG[12.24; 4.98548838168]
Coordinates of the circumscribed circle: U[12.5; 2.27435401165]
Coordinates of the inscribed circle: I[12; 5.84216607228]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.6065653784° = 131°36'20″ = 0.84546406808 rad
∠ B' = β' = 128.0865893213° = 128°5'9″ = 0.90660720917 rad
∠ C' = γ' = 100.3088453003° = 100°18'30″ = 1.39108798811 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 = 20 ; ; c = 25 ; ;

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

p = a+b+c = 19+20+25 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-19)(32-20)(32-25) } ; ; T = sqrt{ 34944 } = 186.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 186.93 }{ 19 } = 19.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 186.93 }{ 20 } = 18.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 186.93 }{ 25 } = 14.95 ; ;

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**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 48° 23'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 51° 54'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-19**2-20**2 }{ 2 * 20 * 19 } ) = 79° 41'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 186.93 }{ 32 } = 5.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 48° 23'40" } = 12.71 ; ;




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