13 22 25 triangle

Acute scalene triangle.

Sides: a = 13   b = 22   c = 25

Area: T = 142.8298568571
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 31.29904452139° = 31°17'26″ = 0.54661212934 rad
Angle ∠ B = β = 61.51553646048° = 61°30'55″ = 1.07436456529 rad
Angle ∠ C = γ = 87.19441901813° = 87°11'39″ = 1.52218257073 rad

Height: ha = 21.9743625934
Height: hb = 12.98444153246
Height: hc = 11.42662854857

Median: ma = 22.63329405955
Median: mb = 16.61332477258
Median: mc = 13.04879883507

Inradius: r = 4.76109522857
Circumradius: R = 12.5155003251

Vertex coordinates: A[25; 0] B[0; 0] C[6.2; 11.42662854857]
Centroid: CG[10.4; 3.80987618286]
Coordinates of the circumscribed circle: U[12.5; 0.61326225368]
Coordinates of the inscribed circle: I[8; 4.76109522857]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.7109554786° = 148°42'34″ = 0.54661212934 rad
∠ B' = β' = 118.4854635395° = 118°29'5″ = 1.07436456529 rad
∠ C' = γ' = 92.80658098187° = 92°48'21″ = 1.52218257073 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 = 13 ; ; b = 22 ; ; c = 25 ; ;

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

p = a+b+c = 13+22+25 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-13)(30-22)(30-25) } ; ; T = sqrt{ 20400 } = 142.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 142.83 }{ 13 } = 21.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 142.83 }{ 22 } = 12.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 142.83 }{ 25 } = 11.43 ; ;

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{ 13**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 31° 17'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 61° 30'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-22**2 }{ 2 * 22 * 13 } ) = 87° 11'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 142.83 }{ 30 } = 4.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 31° 17'26" } = 12.52 ; ;




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