11 21 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 21   c = 28

Area: T = 101.2921658097
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 20.15330742571° = 20°9'11″ = 0.35217375002 rad
Angle ∠ B = β = 41.1287590142° = 41°7'39″ = 0.71878118614 rad
Angle ∠ C = γ = 118.7199335601° = 118°43'10″ = 2.0722043292 rad

Height: ha = 18.41766651085
Height: hb = 9.64768245806
Height: hc = 7.23551184355

Median: ma = 24.1329857024
Median: mb = 18.5
Median: mc = 9.22195444573

Inradius: r = 3.37663886032
Circumradius: R = 15.96438022556

Vertex coordinates: A[28; 0] B[0; 0] C[8.28657142857; 7.23551184355]
Centroid: CG[12.09552380952; 2.41217061452]
Coordinates of the circumscribed circle: U[14; -7.6710917967]
Coordinates of the inscribed circle: I[9; 3.37663886032]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.8476925743° = 159°50'49″ = 0.35217375002 rad
∠ B' = β' = 138.8722409858° = 138°52'21″ = 0.71878118614 rad
∠ C' = γ' = 61.28106643991° = 61°16'50″ = 2.0722043292 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 = 11 ; ; b = 21 ; ; c = 28 ; ;

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

p = a+b+c = 11+21+28 = 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 * (30-11)(30-21)(30-28) } ; ; T = sqrt{ 10260 } = 101.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.29 }{ 11 } = 18.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.29 }{ 21 } = 9.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.29 }{ 28 } = 7.24 ; ;

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{ 11**2-21**2-28**2 }{ 2 * 21 * 28 } ) = 20° 9'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 41° 7'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-21**2 }{ 2 * 21 * 11 } ) = 118° 43'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.29 }{ 30 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 20° 9'11" } = 15.96 ; ;




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