12 16 22 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 16   c = 22

Area: T = 93.6754969976
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 32.15772086093° = 32°9'26″ = 0.56112491685 rad
Angle ∠ B = β = 45.20771662976° = 45°12'26″ = 0.78990138974 rad
Angle ∠ C = γ = 102.6365625093° = 102°38'8″ = 1.79113295877 rad

Height: ha = 15.6122494996
Height: hb = 11.7099371247
Height: hc = 8.51659063615

Median: ma = 18.27656668825
Median: mb = 15.81113883008
Median: mc = 8.88881944173

Inradius: r = 3.7476998799
Circumradius: R = 11.27330220279

Vertex coordinates: A[22; 0] B[0; 0] C[8.45545454545; 8.51659063615]
Centroid: CG[10.15215151515; 2.83986354538]
Coordinates of the circumscribed circle: U[11; -2.46659735686]
Coordinates of the inscribed circle: I[9; 3.7476998799]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.8432791391° = 147°50'34″ = 0.56112491685 rad
∠ B' = β' = 134.7932833702° = 134°47'34″ = 0.78990138974 rad
∠ C' = γ' = 77.3644374907° = 77°21'52″ = 1.79113295877 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 = 16 ; ; c = 22 ; ;

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

p = a+b+c = 12+16+22 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-12)(25-16)(25-22) } ; ; T = sqrt{ 8775 } = 93.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.67 }{ 12 } = 15.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.67 }{ 16 } = 11.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.67 }{ 22 } = 8.52 ; ;

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**2-16**2-22**2 }{ 2 * 16 * 22 } ) = 32° 9'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-12**2-22**2 }{ 2 * 12 * 22 } ) = 45° 12'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-12**2-16**2 }{ 2 * 16 * 12 } ) = 102° 38'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.67 }{ 25 } = 3.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 32° 9'26" } = 11.27 ; ;




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