17 21 29 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 21   c = 29

Area: T = 176.3329769183
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 35.38658397649° = 35°23'9″ = 0.61875994125 rad
Angle ∠ B = β = 45.67105577996° = 45°40'14″ = 0.79771016048 rad
Angle ∠ C = γ = 98.94436024355° = 98°56'37″ = 1.72768916363 rad

Height: ha = 20.74546787274
Height: hb = 16.79333113507
Height: hc = 12.16106737367

Median: ma = 23.84884800354
Median: mb = 21.32548681121
Median: mc = 12.44398553046

Inradius: r = 5.26435751995
Circumradius: R = 14.67884630411

Vertex coordinates: A[29; 0] B[0; 0] C[11.87993103448; 12.16106737367]
Centroid: CG[13.62664367816; 4.05435579122]
Coordinates of the circumscribed circle: U[14.5; -2.2821945935]
Coordinates of the inscribed circle: I[12.5; 5.26435751995]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.6144160235° = 144°36'51″ = 0.61875994125 rad
∠ B' = β' = 134.32994422° = 134°19'46″ = 0.79771016048 rad
∠ C' = γ' = 81.05663975645° = 81°3'23″ = 1.72768916363 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 = 21 ; ; c = 29 ; ;

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

p = a+b+c = 17+21+29 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-17)(33.5-21)(33.5-29) } ; ; T = sqrt{ 31092.19 } = 176.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 176.33 }{ 17 } = 20.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 176.33 }{ 21 } = 16.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 176.33 }{ 29 } = 12.16 ; ;

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**2-21**2-29**2 }{ 2 * 21 * 29 } ) = 35° 23'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 45° 40'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-21**2 }{ 2 * 21 * 17 } ) = 98° 56'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 176.33 }{ 33.5 } = 5.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 35° 23'9" } = 14.68 ; ;




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