Triangle calculator SAS

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


Acute scalene triangle.

Sides: a = 1200   b = 1700   c = 1348.376982341

Area: T = 803770.9698679
Perimeter: p = 4248.376982341
Semiperimeter: s = 2124.18549117

Angle ∠ A = α = 44.53114648378° = 44°31'53″ = 0.77772206822 rad
Angle ∠ B = β = 83.46985351622° = 83°28'7″ = 1.45768007604 rad
Angle ∠ C = γ = 52° = 0.9087571211 rad

Height: ha = 1339.618828113
Height: hb = 945.6132904328
Height: hc = 1192.211144634

Median: ma = 1412.109856181
Median: mb = 952.1329502923
Median: mc = 1307.85111784

Inradius: r = 378.3990301264
Circumradius: R = 855.5532933278

Vertex coordinates: A[1348.376982341; 0] B[0; 0] C[136.4998597893; 1192.211144634]
Centroid: CG[494.9566140433; 397.4043815445]
Coordinates of the circumscribed circle: U[674.1854911703; 526.7310981121]
Coordinates of the inscribed circle: I[424.1854911703; 378.3990301264]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.4698535162° = 135°28'7″ = 0.77772206822 rad
∠ B' = β' = 96.53114648378° = 96°31'53″ = 1.45768007604 rad
∠ C' = γ' = 128° = 0.9087571211 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 = 1200 ; ; b = 1700 ; ; gamma = 52° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 1200**2+1700**2 - 2 * 1200 * 1700 * cos(52° ) } ; ; c = 1348.37 ; ;


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 = 1200 ; ; b = 1700 ; ; c = 1348.37 ; ;

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

p = a+b+c = 1200+1700+1348.37 = 4248.37 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4248.37 }{ 2 } = 2124.18 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2124.18 * (2124.18-1200)(2124.18-1700)(2124.18-1348.37) } ; ; T = sqrt{ 646047770091 } = 803770.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 803770.97 }{ 1200 } = 1339.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 803770.97 }{ 1700 } = 945.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 803770.97 }{ 1348.37 } = 1192.21 ; ;

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{ 1200**2-1700**2-1348.37**2 }{ 2 * 1700 * 1348.37 } ) = 44° 31'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1700**2-1200**2-1348.37**2 }{ 2 * 1200 * 1348.37 } ) = 83° 28'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1348.37**2-1200**2-1700**2 }{ 2 * 1700 * 1200 } ) = 52° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 803770.97 }{ 2124.18 } = 378.39 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1200 }{ 2 * sin 44° 31'53" } = 855.55 ; ;




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