36 43.5 55.5 triangle

Acute scalene triangle.

Sides: a = 36   b = 43.5   c = 55.5

Area: T = 782.5344344294
Perimeter: p = 135
Semiperimeter: s = 67.5

Angle ∠ A = α = 40.41107591034° = 40°24'39″ = 0.70553007996 rad
Angle ∠ B = β = 51.56553491823° = 51°33'55″ = 0.98999851232 rad
Angle ∠ C = γ = 88.02438917143° = 88°1'26″ = 1.53663067308 rad

Height: ha = 43.47441302386
Height: hb = 35.97985905423
Height: hc = 28.19994358304

Median: ma = 46.5
Median: mb = 41.41333130768
Median: mc = 28.70664888135

Inradius: r = 11.5933101397
Circumradius: R = 27.7676512944

Vertex coordinates: A[55.5; 0] B[0; 0] C[22.37883783784; 28.19994358304]
Centroid: CG[25.95994594595; 9.43998119435]
Coordinates of the circumscribed circle: U[27.75; 0.95774659636]
Coordinates of the inscribed circle: I[24; 11.5933101397]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.5899240897° = 139°35'21″ = 0.70553007996 rad
∠ B' = β' = 128.4354650818° = 128°26'5″ = 0.98999851232 rad
∠ C' = γ' = 91.97661082857° = 91°58'34″ = 1.53663067308 rad

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How did we calculate this triangle?

a = 36 ; ; b = 43.5 ; ; c = 55.5 ; ;

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

p = a+b+c = 36+43.5+55.5 = 135 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 135 }{ 2 } = 67.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 67.5 * (67.5-36)(67.5-43.5)(67.5-55.5) } ; ; T = sqrt{ 612360 } = 782.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 782.53 }{ 36 } = 43.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 782.53 }{ 43.5 } = 35.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 782.53 }{ 55.5 } = 28.2 ; ;

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{ 36**2-43.5**2-55.5**2 }{ 2 * 43.5 * 55.5 } ) = 40° 24'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 43.5**2-36**2-55.5**2 }{ 2 * 36 * 55.5 } ) = 51° 33'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 55.5**2-36**2-43.5**2 }{ 2 * 43.5 * 36 } ) = 88° 1'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 782.53 }{ 67.5 } = 11.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 36 }{ 2 * sin 40° 24'39" } = 27.77 ; ;




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