40 36 36 triangle

Acute isosceles triangle.

Sides: a = 40   b = 36   c = 36

Area: T = 598.6655181884
Perimeter: p = 112
Semiperimeter: s = 56

Angle ∠ A = α = 67.49879771918° = 67°29'53″ = 1.17880619404 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 56.25110114041° = 56°15'4″ = 0.98217653566 rad

Height: ha = 29.93332590942
Height: hb = 33.25991767713
Height: hc = 33.25991767713

Median: ma = 29.93332590942
Median: mb = 33.52661092285
Median: mc = 33.52661092285

Inradius: r = 10.69904496765
Circumradius: R = 21.64881605949

Vertex coordinates: A[36; 0] B[0; 0] C[22.22222222222; 33.25991767713]
Centroid: CG[19.40774074074; 11.08663922571]
Coordinates of the circumscribed circle: U[18; 12.02767558861]
Coordinates of the inscribed circle: I[20; 10.69904496765]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.5022022808° = 112°30'7″ = 1.17880619404 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 123.7498988596° = 123°44'56″ = 0.98217653566 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 = 40 ; ; b = 36 ; ; c = 36 ; ;

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

p = a+b+c = 40+36+36 = 112 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 112 }{ 2 } = 56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 56 * (56-40)(56-36)(56-36) } ; ; T = sqrt{ 358400 } = 598.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 598.67 }{ 40 } = 29.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 598.67 }{ 36 } = 33.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 598.67 }{ 36 } = 33.26 ; ;

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{ 40**2-36**2-36**2 }{ 2 * 36 * 36 } ) = 67° 29'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 36**2-40**2-36**2 }{ 2 * 40 * 36 } ) = 56° 15'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 36**2-40**2-36**2 }{ 2 * 36 * 40 } ) = 56° 15'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 598.67 }{ 56 } = 10.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 67° 29'53" } = 21.65 ; ;




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