19 22 26 triangle

Acute scalene triangle.

Sides: a = 19   b = 22   c = 26

Area: T = 204.6854971358
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 45.69990963168° = 45°41'57″ = 0.79875996959 rad
Angle ∠ B = β = 55.96437990453° = 55°57'50″ = 0.97767525553 rad
Angle ∠ C = γ = 78.33771046379° = 78°20'14″ = 1.36772404024 rad

Height: ha = 21.54657864588
Height: hb = 18.60877246689
Height: hc = 15.74549977968

Median: ma = 22.13302959763
Median: mb = 19.93774020374
Median: mc = 15.92216833281

Inradius: r = 6.1109999145
Circumradius: R = 13.27440571131

Vertex coordinates: A[26; 0] B[0; 0] C[10.63546153846; 15.74549977968]
Centroid: CG[12.21215384615; 5.24883325989]
Coordinates of the circumscribed circle: U[13; 2.68333919284]
Coordinates of the inscribed circle: I[11.5; 6.1109999145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.3010903683° = 134°18'3″ = 0.79875996959 rad
∠ B' = β' = 124.0366200955° = 124°2'10″ = 0.97767525553 rad
∠ C' = γ' = 101.6632895362° = 101°39'46″ = 1.36772404024 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 = 19 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 19+22+26 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-19)(33.5-22)(33.5-26) } ; ; T = sqrt{ 41895.94 } = 204.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 204.68 }{ 19 } = 21.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 204.68 }{ 22 } = 18.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 204.68 }{ 26 } = 15.74 ; ;

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{ 19**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 45° 41'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 55° 57'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-19**2-22**2 }{ 2 * 22 * 19 } ) = 78° 20'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 204.68 }{ 33.5 } = 6.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 45° 41'57" } = 13.27 ; ;




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