Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 5979   b = 3600   c = 6979.143328553

Area: T = 10762200
Perimeter: p = 16558.14332855
Semiperimeter: s = 8279.072164277

Angle ∠ A = α = 58.94875438433° = 58°56'51″ = 1.0298828726 rad
Angle ∠ B = β = 31.05224561567° = 31°3'9″ = 0.54219676008 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 3600
Height: hb = 5979
Height: hc = 3084.103346648

Median: ma = 4679.435482164
Median: mb = 6244.072246915
Median: mc = 3489.572164277

Inradius: r = 1299.928835723
Circumradius: R = 3489.572164277

Vertex coordinates: A[6979.143328553; 0] B[0; 0] C[5122.182184059; 3084.103346648]
Centroid: CG[4033.775504204; 1028.034448883]
Coordinates of the circumscribed circle: U[3489.572164277; 0]
Coordinates of the inscribed circle: I[4679.072164277; 1299.928835723]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.0522456157° = 121°3'9″ = 1.0298828726 rad
∠ B' = β' = 148.9487543843° = 148°56'51″ = 0.54219676008 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 = 5979 ; ; b = 3600 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 5979**2+3600**2 - 2 * 5979 * 3600 * cos(90° ) } ; ; c = 6979.14 ; ;


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 = 5979 ; ; b = 3600 ; ; c = 6979.14 ; ;

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

p = a+b+c = 5979+3600+6979.14 = 16558.14 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16558.14 }{ 2 } = 8279.07 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8279.07 * (8279.07-5979)(8279.07-3600)(8279.07-6979.14) } ; ; T = sqrt{ 1.158 * 10**{ 14 } } = 10762200 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10762200 }{ 5979 } = 3600 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10762200 }{ 3600 } = 5979 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10762200 }{ 6979.14 } = 3084.1 ; ;

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{ 5979**2-3600**2-6979.14**2 }{ 2 * 3600 * 6979.14 } ) = 58° 56'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3600**2-5979**2-6979.14**2 }{ 2 * 5979 * 6979.14 } ) = 31° 3'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6979.14**2-5979**2-3600**2 }{ 2 * 3600 * 5979 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10762200 }{ 8279.07 } = 1299.93 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5979 }{ 2 * sin 58° 56'51" } = 3489.57 ; ;




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