Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 849   b = 927   c = 1320

Area: T = 391414.8422049
Perimeter: p = 3096
Semiperimeter: s = 1548

Angle ∠ A = α = 39.77435453316° = 39°46'25″ = 0.69441793212 rad
Angle ∠ B = β = 44.30992617798° = 44°18'33″ = 0.77333425072 rad
Angle ∠ C = γ = 95.91771928886° = 95°55'2″ = 1.67440708252 rad

Height: ha = 922.061087644
Height: hb = 844.4766466125
Height: hc = 593.0532790983

Median: ma = 1058.614430653
Median: mb = 1008.349926985
Median: mc = 595.3769633085

Inradius: r = 252.8521965148
Circumradius: R = 663.5355364782

Vertex coordinates: A[1320; 0] B[0; 0] C[607.5277272727; 593.0532790983]
Centroid: CG[642.5099090909; 197.6844263661]
Coordinates of the circumscribed circle: U[660; -68.40545343295]
Coordinates of the inscribed circle: I[621; 252.8521965148]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.2266454668° = 140°13'35″ = 0.69441793212 rad
∠ B' = β' = 135.691073822° = 135°41'27″ = 0.77333425072 rad
∠ C' = γ' = 84.08328071114° = 84°4'58″ = 1.67440708252 rad

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How did we calculate this triangle?

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 = 849 ; ; b = 927 ; ; c = 1320 ; ;

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

p = a+b+c = 849+927+1320 = 3096 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3096 }{ 2 } = 1548 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1548 * (1548-849)(1548-927)(1548-1320) } ; ; T = sqrt{ 153205578576 } = 391414.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 391414.84 }{ 849 } = 922.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 391414.84 }{ 927 } = 844.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 391414.84 }{ 1320 } = 593.05 ; ;

5. 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{ 849**2-927**2-1320**2 }{ 2 * 927 * 1320 } ) = 39° 46'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 927**2-849**2-1320**2 }{ 2 * 849 * 1320 } ) = 44° 18'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1320**2-849**2-927**2 }{ 2 * 927 * 849 } ) = 95° 55'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 391414.84 }{ 1548 } = 252.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 849 }{ 2 * sin 39° 46'25" } = 663.54 ; ;




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