37.97 44.28 44.28 triangle

Acute isosceles triangle.

Sides: a = 37.97   b = 44.28   c = 44.28

Area: T = 759.4688384451
Perimeter: p = 126.53
Semiperimeter: s = 63.265

Angle ∠ A = α = 50.7766373031° = 50°46'35″ = 0.88662148916 rad
Angle ∠ B = β = 64.61218134845° = 64°36'43″ = 1.1287688881 rad
Angle ∠ C = γ = 64.61218134845° = 64°36'43″ = 1.1287688881 rad

Height: ha = 40.00436020253
Height: hb = 34.30329983943
Height: hc = 34.30329983943

Median: ma = 40.00436020253
Median: mb = 34.88000007184
Median: mc = 34.88000007184

Inradius: r = 12.00545583569
Circumradius: R = 24.50767731496

Vertex coordinates: A[44.28; 0] B[0; 0] C[16.28795946251; 34.30329983943]
Centroid: CG[20.18765315417; 11.43443327981]
Coordinates of the circumscribed circle: U[22.14; 10.50772513154]
Coordinates of the inscribed circle: I[18.985; 12.00545583569]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.2243626969° = 129°13'25″ = 0.88662148916 rad
∠ B' = β' = 115.3888186516° = 115°23'17″ = 1.1287688881 rad
∠ C' = γ' = 115.3888186516° = 115°23'17″ = 1.1287688881 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 = 37.97 ; ; b = 44.28 ; ; c = 44.28 ; ;

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

p = a+b+c = 37.97+44.28+44.28 = 126.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 126.53 }{ 2 } = 63.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 63.27 * (63.27-37.97)(63.27-44.28)(63.27-44.28) } ; ; T = sqrt{ 576792.23 } = 759.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 759.47 }{ 37.97 } = 40 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 759.47 }{ 44.28 } = 34.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 759.47 }{ 44.28 } = 34.3 ; ;

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{ 44.28**2+44.28**2-37.97**2 }{ 2 * 44.28 * 44.28 } ) = 50° 46'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37.97**2+44.28**2-44.28**2 }{ 2 * 37.97 * 44.28 } ) = 64° 36'43" ; ; gamma = 180° - alpha - beta = 180° - 50° 46'35" - 64° 36'43" = 64° 36'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 759.47 }{ 63.27 } = 12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37.97 }{ 2 * sin 50° 46'35" } = 24.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.28**2+2 * 44.28**2 - 37.97**2 } }{ 2 } = 40.004 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.28**2+2 * 37.97**2 - 44.28**2 } }{ 2 } = 34.8 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.28**2+2 * 37.97**2 - 44.28**2 } }{ 2 } = 34.8 ; ;
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