Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Right scalene triangle.

Sides: a = 57   b = 47   c = 73.87882782691

Area: T = 1339.5
Perimeter: p = 177.8788278269
Semiperimeter: s = 88.93991391345

Angle ∠ A = α = 50.49223245571° = 50°29'32″ = 0.88112573105 rad
Angle ∠ B = β = 39.50876754429° = 39°30'28″ = 0.69895390163 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 47
Height: hb = 57
Height: hc = 36.26223502167

Median: ma = 54.9665898519
Median: mb = 61.65442780349
Median: mc = 36.93991391345

Inradius: r = 15.06108608655
Circumradius: R = 36.93991391345

Vertex coordinates: A[73.87882782691; 0] B[0; 0] C[43.97877438798; 36.26223502167]
Centroid: CG[39.28553407163; 12.08774500722]
Coordinates of the circumscribed circle: U[36.93991391345; 0]
Coordinates of the inscribed circle: I[41.93991391345; 15.06108608655]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.5087675443° = 129°30'28″ = 0.88112573105 rad
∠ B' = β' = 140.4922324557° = 140°29'32″ = 0.69895390163 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 57 ; ; b = 47 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 57**2+47**2 - 2 * 57 * 47 * cos(90° ) } ; ; c = 73.88 ; ;


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 = 57 ; ; b = 47 ; ; c = 73.88 ; ;

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

p = a+b+c = 57+47+73.88 = 177.88 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 177.88 }{ 2 } = 88.94 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 88.94 * (88.94-57)(88.94-47)(88.94-73.88) } ; ; T = sqrt{ 1794260.25 } = 1339.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1339.5 }{ 57 } = 47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1339.5 }{ 47 } = 57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1339.5 }{ 73.88 } = 36.26 ; ;

6. 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{ 57**2-47**2-73.88**2 }{ 2 * 47 * 73.88 } ) = 50° 29'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 47**2-57**2-73.88**2 }{ 2 * 57 * 73.88 } ) = 39° 30'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 73.88**2-57**2-47**2 }{ 2 * 47 * 57 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1339.5 }{ 88.94 } = 15.06 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 57 }{ 2 * sin 50° 29'32" } = 36.94 ; ;




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