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: h_a = 21.68772849026
Height: h_b = 20.7444359472
Height: h_c = 18.3510779533

Median: m_a = 21.94331082575
Median: m_b = 21.16601039695
Median: m_c = 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

Calculate another triangle

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

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

6. Inradius

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

7. Circumradius

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

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