18 21 26 triangle

Acute scalene triangle.

Sides: a = 18   b = 21   c = 26

Area: T = 187.6865741334
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 43.43220282875° = 43°25'55″ = 0.75880318944 rad
Angle ∠ B = β = 53.32987880616° = 53°19'44″ = 0.93107629378 rad
Angle ∠ C = γ = 83.23991836509° = 83°14'21″ = 1.45327978214 rad

Height: ha = 20.85439712593
Height: hb = 17.8754832508
Height: hc = 14.4377364718

Median: ma = 21.85217733834
Median: mb = 19.74220870224
Median: mc = 14.61216391962

Inradius: r = 5.77549458872
Circumradius: R = 13.09110317563

Vertex coordinates: A[26; 0] B[0; 0] C[10.75; 14.4377364718]
Centroid: CG[12.25; 4.8122454906]
Coordinates of the circumscribed circle: U[13; 1.54111399819]
Coordinates of the inscribed circle: I[11.5; 5.77549458872]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.5687971712° = 136°34'5″ = 0.75880318944 rad
∠ B' = β' = 126.6711211938° = 126°40'16″ = 0.93107629378 rad
∠ C' = γ' = 96.76108163491° = 96°45'39″ = 1.45327978214 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 = 18 ; ; b = 21 ; ; c = 26 ; ;

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

p = a+b+c = 18+21+26 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-18)(32.5-21)(32.5-26) } ; ; T = sqrt{ 35225.94 } = 187.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 187.69 }{ 18 } = 20.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 187.69 }{ 21 } = 17.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 187.69 }{ 26 } = 14.44 ; ;

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{ 18**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 43° 25'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 53° 19'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-18**2-21**2 }{ 2 * 21 * 18 } ) = 83° 14'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 187.69 }{ 32.5 } = 5.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 43° 25'55" } = 13.09 ; ;




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