19 24 25 triangle

Acute scalene triangle.

Sides: a = 19   b = 24   c = 25

Area: T = 214.2432852856
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ B = β = 64.4322194089° = 64°25'56″ = 1.12545539311 rad
Angle ∠ C = γ = 69.99548099118° = 69°59'41″ = 1.22216398923 rad

Height: ha = 22.5521879248
Height: hb = 17.85435710714
Height: hc = 17.13994282285

Median: ma = 22.58987139962
Median: mb = 18.68215416923
Median: mc = 17.67105970471

Inradius: r = 6.30112603781
Circumradius: R = 13.30326607983

Vertex coordinates: A[25; 0] B[0; 0] C[8.2; 17.13994282285]
Centroid: CG[11.06766666667; 5.71331427428]
Coordinates of the circumscribed circle: U[12.5; 4.55109102731]
Coordinates of the inscribed circle: I[10; 6.30112603781]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ B' = β' = 115.5687805911° = 115°34'4″ = 1.12545539311 rad
∠ C' = γ' = 110.0055190088° = 110°19″ = 1.22216398923 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 = 24 ; ; c = 25 ; ;

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

p = a+b+c = 19+24+25 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-19)(34-24)(34-25) } ; ; T = sqrt{ 45900 } = 214.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 214.24 }{ 19 } = 22.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 214.24 }{ 24 } = 17.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 214.24 }{ 25 } = 17.14 ; ;

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**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 45° 34'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 64° 25'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-19**2-24**2 }{ 2 * 24 * 19 } ) = 69° 59'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 214.24 }{ 34 } = 6.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 45° 34'23" } = 13.3 ; ;




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