Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 1275   b = 300   c = 1309.819868974

Area: T = 191250
Perimeter: p = 2884.819868974
Semiperimeter: s = 1442.409934487

Angle ∠ A = α = 76.75994800848° = 76°45'34″ = 1.34397056596 rad
Angle ∠ B = β = 13.24105199152° = 13°14'26″ = 0.23110906672 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 300
Height: hb = 1275
Height: hc = 292.02551505

Median: ma = 704.5611033552
Median: mb = 1283.793320765
Median: mc = 654.9099344872

Inradius: r = 132.5910655129
Circumradius: R = 654.9099344872

Vertex coordinates: A[1309.819868974; 0] B[0; 0] C[1241.107688963; 292.02551505]
Centroid: CG[850.3098526456; 97.34217168334]
Coordinates of the circumscribed circle: U[654.9099344872; -0]
Coordinates of the inscribed circle: I[1142.409934487; 132.5910655129]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.2410519915° = 103°14'26″ = 1.34397056596 rad
∠ B' = β' = 166.7599480085° = 166°45'34″ = 0.23110906672 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 = 1275 ; ; b = 300 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 1275**2+300**2 - 2 * 1275 * 300 * cos(90° ) } ; ; c = 1309.82 ; ;


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 = 1275 ; ; b = 300 ; ; c = 1309.82 ; ;

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

p = a+b+c = 1275+300+1309.82 = 2884.82 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2884.82 }{ 2 } = 1442.41 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1442.41 * (1442.41-1275)(1442.41-300)(1442.41-1309.82) } ; ; T = sqrt{ 36576562500 } = 191250 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 191250 }{ 1275 } = 300 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 191250 }{ 300 } = 1275 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 191250 }{ 1309.82 } = 292.03 ; ;

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{ 1275**2-300**2-1309.82**2 }{ 2 * 300 * 1309.82 } ) = 76° 45'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 300**2-1275**2-1309.82**2 }{ 2 * 1275 * 1309.82 } ) = 13° 14'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1309.82**2-1275**2-300**2 }{ 2 * 300 * 1275 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 191250 }{ 1442.41 } = 132.59 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1275 }{ 2 * sin 76° 45'34" } = 654.91 ; ;




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