16 21 28 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 21   c = 28

Area: T = 166.5866126373
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 34.51548264544° = 34°30'53″ = 0.60223973624 rad
Angle ∠ B = β = 48.0476537002° = 48°2'48″ = 0.83985702649 rad
Angle ∠ C = γ = 97.43986365436° = 97°26'19″ = 1.70106250263 rad

Height: ha = 20.82332657966
Height: hb = 15.86553453689
Height: hc = 11.89990090267

Median: ma = 23.42200768573
Median: mb = 20.242228248
Median: mc = 12.34990890352

Inradius: r = 5.12657269653
Circumradius: R = 14.11988228048

Vertex coordinates: A[28; 0] B[0; 0] C[10.69664285714; 11.89990090267]
Centroid: CG[12.89988095238; 3.96663363422]
Coordinates of the circumscribed circle: U[14; -1.82878833095]
Coordinates of the inscribed circle: I[11.5; 5.12657269653]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.4855173546° = 145°29'7″ = 0.60223973624 rad
∠ B' = β' = 131.9533462998° = 131°57'12″ = 0.83985702649 rad
∠ C' = γ' = 82.56113634564° = 82°33'41″ = 1.70106250263 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 = 16 ; ; b = 21 ; ; c = 28 ; ;

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

p = a+b+c = 16+21+28 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-16)(32.5-21)(32.5-28) } ; ; T = sqrt{ 27750.94 } = 166.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 166.59 }{ 16 } = 20.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 166.59 }{ 21 } = 15.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 166.59 }{ 28 } = 11.9 ; ;

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{ 16**2-21**2-28**2 }{ 2 * 21 * 28 } ) = 34° 30'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 48° 2'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-21**2 }{ 2 * 21 * 16 } ) = 97° 26'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 166.59 }{ 32.5 } = 5.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 34° 30'53" } = 14.12 ; ;




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