13 17 22 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 17   c = 22

Area: T = 110.3098657865
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 36.14989096752° = 36°8'56″ = 0.63109174948 rad
Angle ∠ B = β = 50.47988036414° = 50°28'44″ = 0.8811021326 rad
Angle ∠ C = γ = 93.37222866834° = 93°22'20″ = 1.63296538327 rad

Height: ha = 16.97105627485
Height: hb = 12.97774891606
Height: hc = 10.02880598059

Median: ma = 18.55439753153
Median: mb = 15.94552187191
Median: mc = 10.39223048454

Inradius: r = 4.24326406871
Circumradius: R = 11.01990806735

Vertex coordinates: A[22; 0] B[0; 0] C[8.27327272727; 10.02880598059]
Centroid: CG[10.09109090909; 3.3432686602]
Coordinates of the circumscribed circle: U[11; -0.64881812161]
Coordinates of the inscribed circle: I[9; 4.24326406871]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.8511090325° = 143°51'4″ = 0.63109174948 rad
∠ B' = β' = 129.5211196359° = 129°31'16″ = 0.8811021326 rad
∠ C' = γ' = 86.62877133166° = 86°37'40″ = 1.63296538327 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 = 17 ; ; c = 22 ; ;

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

p = a+b+c = 13+17+22 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-13)(26-17)(26-22) } ; ; T = sqrt{ 12168 } = 110.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 110.31 }{ 13 } = 16.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 110.31 }{ 17 } = 12.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 110.31 }{ 22 } = 10.03 ; ;

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**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 36° 8'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-13**2-22**2 }{ 2 * 13 * 22 } ) = 50° 28'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-13**2-17**2 }{ 2 * 17 * 13 } ) = 93° 22'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 110.31 }{ 26 } = 4.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 36° 8'56" } = 11.02 ; ;




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