17 23 29 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 23   c = 29

Area: T = 195.4155422882
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 35.87703643042° = 35°52'13″ = 0.6266055961 rad
Angle ∠ B = β = 52.44442226556° = 52°26'39″ = 0.9155324359 rad
Angle ∠ C = γ = 91.68554130402° = 91°41'7″ = 1.66002123336 rad

Height: ha = 22.99900497508
Height: hb = 16.9932645468
Height: hc = 13.4776925716

Median: ma = 24.7543787589
Median: mb = 20.80326440627
Median: mc = 14.09878721799

Inradius: r = 5.6644215156
Circumradius: R = 14.50662756982

Vertex coordinates: A[29; 0] B[0; 0] C[10.36220689655; 13.4776925716]
Centroid: CG[13.12106896552; 4.4922308572]
Coordinates of the circumscribed circle: U[14.5; -0.42766551676]
Coordinates of the inscribed circle: I[11.5; 5.6644215156]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.1329635696° = 144°7'47″ = 0.6266055961 rad
∠ B' = β' = 127.5565777344° = 127°33'21″ = 0.9155324359 rad
∠ C' = γ' = 88.31545869598° = 88°18'53″ = 1.66002123336 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 = 17 ; ; b = 23 ; ; c = 29 ; ;

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

p = a+b+c = 17+23+29 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-17)(34.5-23)(34.5-29) } ; ; T = sqrt{ 38187.19 } = 195.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 195.42 }{ 17 } = 22.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 195.42 }{ 23 } = 16.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 195.42 }{ 29 } = 13.48 ; ;

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{ 17**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 35° 52'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 52° 26'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 91° 41'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 195.42 }{ 34.5 } = 5.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 35° 52'13" } = 14.51 ; ;




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