17 22 29 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 22   c = 29

Area: T = 186.2265669552
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 35.71768160037° = 35°43'1″ = 0.62333760376 rad
Angle ∠ B = β = 49.06772754258° = 49°4'2″ = 0.85663855112 rad
Angle ∠ C = γ = 95.21659085705° = 95°12'57″ = 1.66218311048 rad

Height: ha = 21.90989023002
Height: hb = 16.93296063229
Height: hc = 12.84331496243

Median: ma = 24.29550612265
Median: mb = 21.07113075057
Median: mc = 13.27659180474

Inradius: r = 5.47772255751
Circumradius: R = 14.56602913203

Vertex coordinates: A[29; 0] B[0; 0] C[11.13879310345; 12.84331496243]
Centroid: CG[13.37993103448; 4.28110498748]
Coordinates of the circumscribed circle: U[14.5; -1.32436628473]
Coordinates of the inscribed circle: I[12; 5.47772255751]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.2833183996° = 144°16'59″ = 0.62333760376 rad
∠ B' = β' = 130.9332724574° = 130°55'58″ = 0.85663855112 rad
∠ C' = γ' = 84.78440914295° = 84°47'3″ = 1.66218311048 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 = 22 ; ; c = 29 ; ;

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

p = a+b+c = 17+22+29 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-17)(34-22)(34-29) } ; ; T = sqrt{ 34680 } = 186.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 186.23 }{ 17 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 186.23 }{ 22 } = 16.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 186.23 }{ 29 } = 12.84 ; ;

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**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 35° 43'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 49° 4'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-22**2 }{ 2 * 22 * 17 } ) = 95° 12'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 186.23 }{ 34 } = 5.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 35° 43'1" } = 14.56 ; ;




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