12 17 22 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 17   c = 22

Area: T = 101.2199987648
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 32.76437577589° = 32°45'50″ = 0.57218354482 rad
Angle ∠ B = β = 50.05554864597° = 50°3'20″ = 0.87436330474 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 16.8676664608
Height: hb = 11.90658808998
Height: hc = 9.21999988771

Median: ma = 18.72216452268
Median: mb = 15.54883118055
Median: mc = 9.77224101428

Inradius: r = 3.96986269666
Circumradius: R = 11.08769578749

Vertex coordinates: A[22; 0] B[0; 0] C[7.70545454545; 9.21999988771]
Centroid: CG[9.90215151515; 3.06766662924]
Coordinates of the circumscribed circle: U[11; -1.38658697344]
Coordinates of the inscribed circle: I[8.5; 3.96986269666]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.2366242241° = 147°14'10″ = 0.57218354482 rad
∠ B' = β' = 129.945451354° = 129°56'40″ = 0.87436330474 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 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 = 12 ; ; b = 17 ; ; c = 22 ; ;

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

p = a+b+c = 12+17+22 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-12)(25.5-17)(25.5-22) } ; ; T = sqrt{ 10241.44 } = 101.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.2 }{ 12 } = 16.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.2 }{ 17 } = 11.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.2 }{ 22 } = 9.2 ; ;

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{ 12**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 32° 45'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-12**2-22**2 }{ 2 * 12 * 22 } ) = 50° 3'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-12**2-17**2 }{ 2 * 17 * 12 } ) = 97° 10'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.2 }{ 25.5 } = 3.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 32° 45'50" } = 11.09 ; ;




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