13 17 29 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 17   c = 29

Area: T = 55.15660286823
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 12.93297789339° = 12°55'47″ = 0.2265667214 rad
Angle ∠ B = β = 17.01439737181° = 17°50″ = 0.29769498602 rad
Angle ∠ C = γ = 150.0566247348° = 150°3'23″ = 2.61989755794 rad

Height: ha = 8.48655428742
Height: hb = 6.48989445509
Height: hc = 3.80438640471

Median: ma = 22.86437267303
Median: mb = 20.80326440627
Median: mc = 4.33301270189

Inradius: r = 1.87696958875
Circumradius: R = 29.04994083472

Vertex coordinates: A[29; 0] B[0; 0] C[12.43110344828; 3.80438640471]
Centroid: CG[13.81103448276; 1.26879546824]
Coordinates of the circumscribed circle: U[14.5; -25.17217723913]
Coordinates of the inscribed circle: I[12.5; 1.87696958875]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.0770221066° = 167°4'13″ = 0.2265667214 rad
∠ B' = β' = 162.9866026282° = 162°59'10″ = 0.29769498602 rad
∠ C' = γ' = 29.9443752652° = 29°56'38″ = 2.61989755794 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 = 13 ; ; b = 17 ; ; c = 29 ; ;

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

p = a+b+c = 13+17+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-13)(29.5-17)(29.5-29) } ; ; T = sqrt{ 3042.19 } = 55.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.16 }{ 13 } = 8.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.16 }{ 17 } = 6.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.16 }{ 29 } = 3.8 ; ;

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{ 13**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 12° 55'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-13**2-29**2 }{ 2 * 13 * 29 } ) = 17° 50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-13**2-17**2 }{ 2 * 17 * 13 } ) = 150° 3'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.16 }{ 29.5 } = 1.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 12° 55'47" } = 29.05 ; ;




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