36 37 41 triangle

Acute scalene triangle.

Sides: a = 36   b = 37   c = 41

Area: T = 618.9022253995
Perimeter: p = 114
Semiperimeter: s = 57

Angle ∠ A = α = 54.68219503538° = 54°40'55″ = 0.95443800751 rad
Angle ∠ B = β = 56.9954779568° = 56°59'41″ = 0.99547465599 rad
Angle ∠ C = γ = 68.32332700781° = 68°19'24″ = 1.19224660186 rad

Height: ha = 34.38334585553
Height: hb = 33.45441758916
Height: hc = 30.19903538534

Median: ma = 34.65554469023
Median: mb = 33.85663140345
Median: mc = 30.20334766211

Inradius: r = 10.85879342806
Circumradius: R = 22.06600262996

Vertex coordinates: A[41; 0] B[0; 0] C[19.61097560976; 30.19903538534]
Centroid: CG[20.20332520325; 10.06334512845]
Coordinates of the circumscribed circle: U[20.5; 8.14882980025]
Coordinates of the inscribed circle: I[20; 10.85879342806]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.3188049646° = 125°19'5″ = 0.95443800751 rad
∠ B' = β' = 123.0055220432° = 123°19″ = 0.99547465599 rad
∠ C' = γ' = 111.6776729922° = 111°40'36″ = 1.19224660186 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 = 36 ; ; b = 37 ; ; c = 41 ; ;

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

p = a+b+c = 36+37+41 = 114 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 114 }{ 2 } = 57 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 57 * (57-36)(57-37)(57-41) } ; ; T = sqrt{ 383040 } = 618.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 618.9 }{ 36 } = 34.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 618.9 }{ 37 } = 33.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 618.9 }{ 41 } = 30.19 ; ;

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{ 37**2+41**2-36**2 }{ 2 * 37 * 41 } ) = 54° 40'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 36**2+41**2-37**2 }{ 2 * 36 * 41 } ) = 56° 59'41" ; ; gamma = 180° - alpha - beta = 180° - 54° 40'55" - 56° 59'41" = 68° 19'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 618.9 }{ 57 } = 10.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 36 }{ 2 * sin 54° 40'55" } = 22.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 37**2+2 * 41**2 - 36**2 } }{ 2 } = 34.655 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 41**2+2 * 36**2 - 37**2 } }{ 2 } = 33.856 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 37**2+2 * 36**2 - 41**2 } }{ 2 } = 30.203 ; ;
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