Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 736   b = 915   c = 184.084381849

Area: T = 17622.56331861
Perimeter: p = 1835.084381849
Semiperimeter: s = 917.5421909245

Angle ∠ A = α = 12.07883163573° = 12°4'42″ = 0.21108063885 rad
Angle ∠ B = β = 164.9221683643° = 164°55'18″ = 2.87884263875 rad
Angle ∠ C = γ = 3° = 0.05223598776 rad

Height: ha = 47.88773999623
Height: hb = 38.51992637948
Height: hc = 191.4622381981

Median: ma = 547.8432975783
Median: mb = 280.1522058916
Median: mc = 825.2220447482

Inradius: r = 19.20662760388
Circumradius: R = 1758.674445352

Vertex coordinates: A[184.084381849; 0] B[0; 0] C[-710.666036634; 191.4622381981]
Centroid: CG[-175.526551595; 63.82107939938]
Coordinates of the circumscribed circle: U[92.04219092449; 1756.26442513]
Coordinates of the inscribed circle: I[2.54219092449; 19.20662760388]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9221683643° = 167°55'18″ = 0.21108063885 rad
∠ B' = β' = 15.07883163573° = 15°4'42″ = 2.87884263875 rad
∠ C' = γ' = 177° = 0.05223598776 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 = 736 ; ; b = 915 ; ; gamma = 3° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 736**2+915**2 - 2 * 736 * 915 * cos(3° ) } ; ; c = 184.08 ; ;


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 = 736 ; ; b = 915 ; ; c = 184.08 ; ;

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

p = a+b+c = 736+915+184.08 = 1835.08 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1835.08 }{ 2 } = 917.54 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 917.54 * (917.54-736)(917.54-915)(917.54-184.08) } ; ; T = sqrt{ 310554733.25 } = 17622.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17622.56 }{ 736 } = 47.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17622.56 }{ 915 } = 38.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17622.56 }{ 184.08 } = 191.46 ; ;

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{ 736**2-915**2-184.08**2 }{ 2 * 915 * 184.08 } ) = 12° 4'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 915**2-736**2-184.08**2 }{ 2 * 736 * 184.08 } ) = 164° 55'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 184.08**2-736**2-915**2 }{ 2 * 915 * 736 } ) = 3° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17622.56 }{ 917.54 } = 19.21 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 736 }{ 2 * sin 12° 4'42" } = 1758.67 ; ;




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