17 26 29 triangle

Acute scalene triangle.

Sides: a = 17   b = 26   c = 29

Area: T = 218.8154990346
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 35.47994634727° = 35°28'46″ = 0.61992334544 rad
Angle ∠ B = β = 62.58440932158° = 62°35'3″ = 1.0922298486 rad
Angle ∠ C = γ = 81.93664433115° = 81°56'11″ = 1.43300607132 rad

Height: ha = 25.74329400407
Height: hb = 16.83219223343
Height: hc = 15.09106889894

Median: ma = 26.19663737949
Median: mb = 19.98997487421
Median: mc = 16.5

Inradius: r = 6.07881941763
Circumradius: R = 14.64547919082

Vertex coordinates: A[29; 0] B[0; 0] C[7.82875862069; 15.09106889894]
Centroid: CG[12.2765862069; 5.03302296631]
Coordinates of the circumscribed circle: U[14.5; 2.05442468287]
Coordinates of the inscribed circle: I[10; 6.07881941763]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.5210536527° = 144°31'14″ = 0.61992334544 rad
∠ B' = β' = 117.4165906784° = 117°24'57″ = 1.0922298486 rad
∠ C' = γ' = 98.06435566885° = 98°3'49″ = 1.43300607132 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 = 26 ; ; c = 29 ; ;

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

p = a+b+c = 17+26+29 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-17)(36-26)(36-29) } ; ; T = sqrt{ 47880 } = 218.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 218.81 }{ 17 } = 25.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 218.81 }{ 26 } = 16.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 218.81 }{ 29 } = 15.09 ; ;

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**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 35° 28'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 62° 35'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-26**2 }{ 2 * 26 * 17 } ) = 81° 56'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 218.81 }{ 36 } = 6.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 35° 28'46" } = 14.64 ; ;




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