11 21 29 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 21   c = 29

Area: T = 92.06107815522
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 17.59878581455° = 17°35'52″ = 0.30771405659 rad
Angle ∠ B = β = 35.25326937328° = 35°15'10″ = 0.61552755758 rad
Angle ∠ C = γ = 127.1499448122° = 127°8'58″ = 2.21991765118 rad

Height: ha = 16.73883239186
Height: hb = 8.76876934812
Height: hc = 6.34990194174

Median: ma = 24.71333567125
Median: mb = 19.2554869514
Median: mc = 8.41113019206

Inradius: r = 3.01883862804
Circumradius: R = 18.19217855982

Vertex coordinates: A[29; 0] B[0; 0] C[8.98327586207; 6.34990194174]
Centroid: CG[12.66109195402; 2.11663398058]
Coordinates of the circumscribed circle: U[14.5; -10.98659484457]
Coordinates of the inscribed circle: I[9.5; 3.01883862804]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.4022141855° = 162°24'8″ = 0.30771405659 rad
∠ B' = β' = 144.7477306267° = 144°44'50″ = 0.61552755758 rad
∠ C' = γ' = 52.85105518783° = 52°51'2″ = 2.21991765118 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 = 29 ; ;

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

p = a+b+c = 11+21+29 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-11)(30.5-21)(30.5-29) } ; ; T = sqrt{ 8475.19 } = 92.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 92.06 }{ 11 } = 16.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 92.06 }{ 21 } = 8.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 92.06 }{ 29 } = 6.35 ; ;

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**2-29**2 }{ 2 * 21 * 29 } ) = 17° 35'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-11**2-29**2 }{ 2 * 11 * 29 } ) = 35° 15'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-11**2-21**2 }{ 2 * 21 * 11 } ) = 127° 8'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 92.06 }{ 30.5 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 17° 35'52" } = 18.19 ; ;




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