17 20 29 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 20   c = 29

Area: T = 165.6998521418
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 34.84661094173° = 34°50'46″ = 0.60881793408 rad
Angle ∠ B = β = 42.23774732352° = 42°14'15″ = 0.73771829757 rad
Angle ∠ C = γ = 102.9166417347° = 102°54'59″ = 1.79662303371 rad

Height: ha = 19.49439436962
Height: hb = 16.57698521418
Height: hc = 11.42774842357

Median: ma = 23.41547389479
Median: mb = 21.56438586528
Median: mc = 11.58766302263

Inradius: r = 5.02111673157
Circumradius: R = 14.87664151841

Vertex coordinates: A[29; 0] B[0; 0] C[12.58662068966; 11.42774842357]
Centroid: CG[13.86220689655; 3.80991614119]
Coordinates of the circumscribed circle: U[14.5; -3.32553163353]
Coordinates of the inscribed circle: I[13; 5.02111673157]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.1543890583° = 145°9'14″ = 0.60881793408 rad
∠ B' = β' = 137.7632526765° = 137°45'45″ = 0.73771829757 rad
∠ C' = γ' = 77.08435826525° = 77°5'1″ = 1.79662303371 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 = 20 ; ; c = 29 ; ;

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

p = a+b+c = 17+20+29 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-17)(33-20)(33-29) } ; ; T = sqrt{ 27456 } = 165.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 165.7 }{ 17 } = 19.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 165.7 }{ 20 } = 16.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 165.7 }{ 29 } = 11.43 ; ;

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**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 34° 50'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 42° 14'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-20**2 }{ 2 * 20 * 17 } ) = 102° 54'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 165.7 }{ 33 } = 5.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 50'46" } = 14.88 ; ;




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