17 28 29 triangle

Acute scalene triangle.

Sides: a = 17   b = 28   c = 29

Area: T = 230.825460874
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 34.64880267617° = 34°38'53″ = 0.60547221463 rad
Angle ∠ B = β = 69.45768450907° = 69°27'25″ = 1.21222506349 rad
Angle ∠ C = γ = 75.89551281476° = 75°53'42″ = 1.32546198724 rad

Height: ha = 27.15658363224
Height: hb = 16.48774720529
Height: hc = 15.91989385338

Median: ma = 27.20875357208
Median: mb = 19.20993727123
Median: mc = 18.06223918682

Inradius: r = 6.23985029389
Circumradius: R = 14.95107455849

Vertex coordinates: A[29; 0] B[0; 0] C[5.96655172414; 15.91989385338]
Centroid: CG[11.65551724138; 5.30663128446]
Coordinates of the circumscribed circle: U[14.5; 3.64334590081]
Coordinates of the inscribed circle: I[9; 6.23985029389]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.3521973238° = 145°21'7″ = 0.60547221463 rad
∠ B' = β' = 110.5433154909° = 110°32'35″ = 1.21222506349 rad
∠ C' = γ' = 104.1054871852° = 104°6'18″ = 1.32546198724 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 = 28 ; ; c = 29 ; ;

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

p = a+b+c = 17+28+29 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-17)(37-28)(37-29) } ; ; T = sqrt{ 53280 } = 230.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 230.82 }{ 17 } = 27.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 230.82 }{ 28 } = 16.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 230.82 }{ 29 } = 15.92 ; ;

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**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 34° 38'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 69° 27'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-28**2 }{ 2 * 28 * 17 } ) = 75° 53'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 230.82 }{ 37 } = 6.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 38'53" } = 14.95 ; ;




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