22 23 26 triangle

Acute scalene triangle.

Sides: a = 22   b = 23   c = 26

Area: T = 238.5660133928
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 52.92662286621° = 52°55'34″ = 0.92437369508 rad
Angle ∠ B = β = 56.52549762939° = 56°31'30″ = 0.98765469459 rad
Angle ∠ C = γ = 70.5498795044° = 70°32'56″ = 1.23113087568 rad

Height: ha = 21.68772849026
Height: hb = 20.7444359472
Height: hc = 18.3510779533

Median: ma = 21.94331082575
Median: mb = 21.16601039695
Median: mc = 18.37111730709

Inradius: r = 6.72200037726
Circumradius: R = 13.78768802546

Vertex coordinates: A[26; 0] B[0; 0] C[12.13546153846; 18.3510779533]
Centroid: CG[12.71215384615; 6.1176926511]
Coordinates of the circumscribed circle: U[13; 4.59110856184]
Coordinates of the inscribed circle: I[12.5; 6.72200037726]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.0743771338° = 127°4'26″ = 0.92437369508 rad
∠ B' = β' = 123.4755023706° = 123°28'30″ = 0.98765469459 rad
∠ C' = γ' = 109.4511204956° = 109°27'4″ = 1.23113087568 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 = 22 ; ; b = 23 ; ; c = 26 ; ;

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

p = a+b+c = 22+23+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 * (35.5-22)(35.5-23)(35.5-26) } ; ; T = sqrt{ 56910.94 } = 238.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 238.56 }{ 22 } = 21.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 238.56 }{ 23 } = 20.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 238.56 }{ 26 } = 18.35 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 23**2+26**2-22**2 }{ 2 * 23 * 26 } ) = 52° 55'34" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 22**2+26**2-23**2 }{ 2 * 22 * 26 } ) = 56° 31'30" ; ; gamma = 180° - alpha - beta = 180° - 52° 55'34" - 56° 31'30" = 70° 32'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 238.56 }{ 35.5 } = 6.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 22 }{ 2 * sin 52° 55'34" } = 13.79 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 26**2 - 22**2 } }{ 2 } = 21.943 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 22**2 - 23**2 } }{ 2 } = 21.16 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 22**2 - 26**2 } }{ 2 } = 18.371 ; ;
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