21 24 26 triangle

Acute scalene triangle.

Sides: a = 21   b = 24   c = 26

Area: T = 237.1422230528
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 49.4770479683° = 49°28'14″ = 0.8633422753 rad
Angle ∠ B = β = 60.30224684279° = 60°18'9″ = 1.05224766211 rad
Angle ∠ C = γ = 70.22770518891° = 70°13'37″ = 1.22656932794 rad

Height: ha = 22.5854974336
Height: hb = 19.7621852544
Height: hc = 18.24217100406

Median: ma = 22.71101298984
Median: mb = 20.35992730715
Median: mc = 18.42655257727

Inradius: r = 6.68800628318
Circumradius: R = 13.81444943341

Vertex coordinates: A[26; 0] B[0; 0] C[10.40438461538; 18.24217100406]
Centroid: CG[12.13546153846; 6.08105700135]
Coordinates of the circumscribed circle: U[13; 4.67333557221]
Coordinates of the inscribed circle: I[11.5; 6.68800628318]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.5329520317° = 130°31'46″ = 0.8633422753 rad
∠ B' = β' = 119.6987531572° = 119°41'51″ = 1.05224766211 rad
∠ C' = γ' = 109.7732948111° = 109°46'23″ = 1.22656932794 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 = 24 ; ; c = 26 ; ;

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

p = a+b+c = 21+24+26 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-21)(35.5-24)(35.5-26) } ; ; T = sqrt{ 56236.44 } = 237.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 237.14 }{ 21 } = 22.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 237.14 }{ 24 } = 19.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 237.14 }{ 26 } = 18.24 ; ;

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**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 49° 28'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 60° 18'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-21**2-24**2 }{ 2 * 24 * 21 } ) = 70° 13'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 237.14 }{ 35.5 } = 6.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 49° 28'14" } = 13.81 ; ;




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