11 17 21 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 17   c = 21

Area: T = 93.17882565838
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 31.46769762933° = 31°28'1″ = 0.5499202342 rad
Angle ∠ B = β = 53.77884533802° = 53°46'42″ = 0.93986110781 rad
Angle ∠ C = γ = 94.75545703266° = 94°45'16″ = 1.65437792335 rad

Height: ha = 16.94215011971
Height: hb = 10.96221478334
Height: hc = 8.87441196746

Median: ma = 18.29661744635
Median: mb = 14.44881832768
Median: mc = 9.7343961167

Inradius: r = 3.80331941463
Circumradius: R = 10.53662563756

Vertex coordinates: A[21; 0] B[0; 0] C[6.5; 8.87441196746]
Centroid: CG[9.16766666667; 2.95880398915]
Coordinates of the circumscribed circle: U[10.5; -0.87333260632]
Coordinates of the inscribed circle: I[7.5; 3.80331941463]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.5333023707° = 148°31'59″ = 0.5499202342 rad
∠ B' = β' = 126.222154662° = 126°13'18″ = 0.93986110781 rad
∠ C' = γ' = 85.24554296734° = 85°14'44″ = 1.65437792335 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 = 17 ; ; c = 21 ; ;

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

p = a+b+c = 11+17+21 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-11)(24.5-17)(24.5-21) } ; ; T = sqrt{ 8682.19 } = 93.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.18 }{ 11 } = 16.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.18 }{ 17 } = 10.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.18 }{ 21 } = 8.87 ; ;

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**2-17**2-21**2 }{ 2 * 17 * 21 } ) = 31° 28'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-11**2-21**2 }{ 2 * 11 * 21 } ) = 53° 46'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-11**2-17**2 }{ 2 * 17 * 11 } ) = 94° 45'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.18 }{ 24.5 } = 3.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 31° 28'1" } = 10.54 ; ;




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