Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 13.2   b = 5.3   c = 9.32883580382

Area: T = 19.81328901676
Perimeter: p = 27.82883580382
Semiperimeter: s = 13.91441790191

Angle ∠ A = α = 126.728761653° = 126°43'39″ = 2.21218141616 rad
Angle ∠ B = β = 18.77223834702° = 18°46'21″ = 0.32876399 rad
Angle ∠ C = γ = 34.5° = 34°30' = 0.60221385919 rad

Height: ha = 3.00219530557
Height: hb = 7.47765623274
Height: hc = 4.24878837297

Median: ma = 3.74108731393
Median: mb = 11.11878519438
Median: mc = 8.91112532271

Inradius: r = 1.42439352635
Circumradius: R = 8.23546886652

Vertex coordinates: A[9.32883580382; 0] B[0; 0] C[12.49878191625; 4.24878837297]
Centroid: CG[7.27553924002; 1.41659612432]
Coordinates of the circumscribed circle: U[4.66441790191; 6.78664225841]
Coordinates of the inscribed circle: I[8.61441790191; 1.42439352635]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 53.27223834702° = 53°16'21″ = 2.21218141616 rad
∠ B' = β' = 161.228761653° = 161°13'39″ = 0.32876399 rad
∠ C' = γ' = 145.5° = 145°30' = 0.60221385919 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 = 13.2 ; ; b = 5.3 ; ; gamma = 34° 30' ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 13.2**2+5.3**2 - 2 * 13.2 * 5.3 * cos(34° 30') } ; ; c = 9.33 ; ;


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 = 13.2 ; ; b = 5.3 ; ; c = 9.33 ; ;

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

p = a+b+c = 13.2+5.3+9.33 = 27.83 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.83 }{ 2 } = 13.91 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.91 * (13.91-13.2)(13.91-5.3)(13.91-9.33) } ; ; T = sqrt{ 392.55 } = 19.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.81 }{ 13.2 } = 3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.81 }{ 5.3 } = 7.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.81 }{ 9.33 } = 4.25 ; ;

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{ 13.2**2-5.3**2-9.33**2 }{ 2 * 5.3 * 9.33 } ) = 126° 43'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.3**2-13.2**2-9.33**2 }{ 2 * 13.2 * 9.33 } ) = 18° 46'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.33**2-13.2**2-5.3**2 }{ 2 * 5.3 * 13.2 } ) = 34° 30' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.81 }{ 13.91 } = 1.42 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13.2 }{ 2 * sin 126° 43'39" } = 8.23 ; ;




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