40 60 60 triangle

Acute isosceles triangle.

Sides: a = 40   b = 60   c = 60

Area: T = 1131.37108499
Perimeter: p = 160
Semiperimeter: s = 80

Angle ∠ A = α = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 70.52987793655° = 70°31'44″ = 1.23109594173 rad

Height: ha = 56.56985424949
Height: hb = 37.71223616633
Height: hc = 37.71223616633

Median: ma = 56.56985424949
Median: mb = 41.23110562562
Median: mc = 41.23110562562

Inradius: r = 14.14221356237
Circumradius: R = 31.82198051534

Vertex coordinates: A[60; 0] B[0; 0] C[13.33333333333; 37.71223616633]
Centroid: CG[24.44444444444; 12.57107872211]
Coordinates of the circumscribed circle: U[30; 10.60766017178]
Coordinates of the inscribed circle: I[20; 14.14221356237]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad

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How did we calculate this triangle?

a = 40 ; ; b = 60 ; ; c = 60 ; ;

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

p = a+b+c = 40+60+60 = 160 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 160 }{ 2 } = 80 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 80 * (80-40)(80-60)(80-60) } ; ; T = sqrt{ 1280000 } = 1131.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1131.37 }{ 40 } = 56.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1131.37 }{ 60 } = 37.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1131.37 }{ 60 } = 37.71 ; ;

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**2-60**2-60**2 }{ 2 * 60 * 60 } ) = 38° 56'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60**2-40**2-60**2 }{ 2 * 40 * 60 } ) = 70° 31'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 60**2-40**2-60**2 }{ 2 * 60 * 40 } ) = 70° 31'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1131.37 }{ 80 } = 14.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 38° 56'33" } = 31.82 ; ;




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