40 66 66 triangle

Acute isosceles triangle.

Sides: a = 40   b = 66   c = 66

Area: T = 1257.935481548
Perimeter: p = 172
Semiperimeter: s = 86

Angle ∠ A = α = 35.27994027885° = 35°16'46″ = 0.61657417368 rad
Angle ∠ B = β = 72.36602986058° = 72°21'37″ = 1.26329254584 rad
Angle ∠ C = γ = 72.36602986058° = 72°21'37″ = 1.26329254584 rad

Height: ha = 62.89767407741
Height: hb = 38.11992368328
Height: hc = 38.11992368328

Median: ma = 62.89767407741
Median: mb = 43.46326276242
Median: mc = 43.46326276242

Inradius: r = 14.62771490172
Circumradius: R = 34.62881853908

Vertex coordinates: A[66; 0] B[0; 0] C[12.12112121212; 38.11992368328]
Centroid: CG[26.04404040404; 12.70664122776]
Coordinates of the circumscribed circle: U[33; 10.49333895124]
Coordinates of the inscribed circle: I[20; 14.62771490172]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.7210597212° = 144°43'14″ = 0.61657417368 rad
∠ B' = β' = 107.6439701394° = 107°38'23″ = 1.26329254584 rad
∠ C' = γ' = 107.6439701394° = 107°38'23″ = 1.26329254584 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 = 66 ; ; c = 66 ; ;

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

p = a+b+c = 40+66+66 = 172 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 172 }{ 2 } = 86 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 86 * (86-40)(86-66)(86-66) } ; ; T = sqrt{ 1582400 } = 1257.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1257.93 }{ 40 } = 62.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1257.93 }{ 66 } = 38.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1257.93 }{ 66 } = 38.12 ; ;

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**2-66**2-66**2 }{ 2 * 66 * 66 } ) = 35° 16'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 66**2-40**2-66**2 }{ 2 * 40 * 66 } ) = 72° 21'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 66**2-40**2-66**2 }{ 2 * 66 * 40 } ) = 72° 21'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1257.93 }{ 86 } = 14.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 35° 16'46" } = 34.63 ; ;

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