21 26 29 triangle

Acute scalene triangle.

Sides: a = 21   b = 26   c = 29

Area: T = 264.1366328437
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 44.47773191989° = 44°28'38″ = 0.77662756625 rad
Angle ∠ B = β = 60.1632821003° = 60°9'46″ = 1.05500393138 rad
Angle ∠ C = γ = 75.36598597981° = 75°21'35″ = 1.31552776773 rad

Height: ha = 25.15658408035
Height: hb = 20.31881791105
Height: hc = 18.21662985129

Median: ma = 25.46107541129
Median: mb = 21.72655609824
Median: mc = 18.66114576065

Inradius: r = 6.95109560115
Circumradius: R = 14.98765791784

Vertex coordinates: A[29; 0] B[0; 0] C[10.44882758621; 18.21662985129]
Centroid: CG[13.14994252874; 6.07220995043]
Coordinates of the circumscribed circle: U[14.5; 3.78878167154]
Coordinates of the inscribed circle: I[12; 6.95109560115]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5232680801° = 135°31'22″ = 0.77662756625 rad
∠ B' = β' = 119.8377178997° = 119°50'14″ = 1.05500393138 rad
∠ C' = γ' = 104.6440140202° = 104°38'25″ = 1.31552776773 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 = 21 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 21+26+29 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-21)(38-26)(38-29) } ; ; T = sqrt{ 69768 } = 264.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 264.14 }{ 21 } = 25.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 264.14 }{ 26 } = 20.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 264.14 }{ 29 } = 18.22 ; ;

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{ 21**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 44° 28'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-21**2-29**2 }{ 2 * 21 * 29 } ) = 60° 9'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-21**2-26**2 }{ 2 * 26 * 21 } ) = 75° 21'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 264.14 }{ 38 } = 6.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 44° 28'38" } = 14.99 ; ;




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