11 23 29 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 23   c = 29

Area: T = 117.1421741066
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 20.5643765192° = 20°33'50″ = 0.35989054092 rad
Angle ∠ B = β = 47.25991563765° = 47°15'33″ = 0.82548278805 rad
Angle ∠ C = γ = 112.1777078431° = 112°10'37″ = 1.95878593639 rad

Height: ha = 21.29884983757
Height: hb = 10.18662383536
Height: hc = 8.07987407632

Median: ma = 25.58880831638
Median: mb = 18.6754849397
Median: mc = 10.71221426428

Inradius: r = 3.71987854307
Circumradius: R = 15.65883808923

Vertex coordinates: A[29; 0] B[0; 0] C[7.46655172414; 8.07987407632]
Centroid: CG[12.15551724138; 2.69329135877]
Coordinates of the circumscribed circle: U[14.5; -5.91105746056]
Coordinates of the inscribed circle: I[8.5; 3.71987854307]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.4366234808° = 159°26'10″ = 0.35989054092 rad
∠ B' = β' = 132.7410843623° = 132°44'27″ = 0.82548278805 rad
∠ C' = γ' = 67.82329215686° = 67°49'23″ = 1.95878593639 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 = 23 ; ; c = 29 ; ;

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

p = a+b+c = 11+23+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-11)(31.5-23)(31.5-29) } ; ; T = sqrt{ 13722.19 } = 117.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117.14 }{ 11 } = 21.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117.14 }{ 23 } = 10.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117.14 }{ 29 } = 8.08 ; ;

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**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 20° 33'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-11**2-29**2 }{ 2 * 11 * 29 } ) = 47° 15'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-11**2-23**2 }{ 2 * 23 * 11 } ) = 112° 10'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117.14 }{ 31.5 } = 3.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 20° 33'50" } = 15.66 ; ;




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