Triangle calculator SSA

Please enter two sides and a non-included angle
°


Right scalene triangle.

Sides: a = 23770.2   b = 25920   c = 10335.56992615

Area: T = 122839274.23
Perimeter: p = 60025.76992615
Semiperimeter: s = 30012.88546308

Angle ∠ A = α = 66.55000159207° = 66°30' = 1.16106442304 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 23.54999840793° = 23°30' = 0.41101520963 rad

Height: ha = 10335.56992615
Height: hb = 9478.339906098
Height: hc = 23770.2

Median: ma = 15750.54326564
Median: mb = 12960
Median: mc = 24325.46882592

Inradius: r = 4092.885463077
Circumradius: R = 12960

Vertex coordinates: A[10335.56992615; 0] B[0; 0] C[-0; 23770.2]
Centroid: CG[3445.198975385; 7923.4]
Coordinates of the circumscribed circle: U[5167.785463077; 11885.1]
Coordinates of the inscribed circle: I[4092.885463077; 4092.885463077]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 113.5499984079° = 113°30' = 1.16106442304 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 156.5500015921° = 156°30' = 0.41101520963 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 23770.2 ; ; b = 25920 ; ; beta = 90° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 25920**2 = 23770.2**2 + c**2 -2 * 25920 * c * cos (90° ) ; ; ; ; c**2 -106823991.96 =0 ; ; p=1; q=-2.91100993451E-12; r=-106823991.96 ; ; D = q**2 - 4pr = 0**2 - 4 * 1 * (-106823991.96) = 427295967.84 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ ± sqrt{ 427295967.84 } }{ 2 } ; ; c_{1,2} = 1.45550496725E-12 ± 10335.5692615 ; ;
c_{1} = 10335.5692615 ; ; c_{2} = -10335.5692615 ; ; ; ; (c -10335.5692615) (c +10335.5692615) = 0 ; ; ; ; c>0 ; ;


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 = 23770.2 ; ; b = 25920 ; ; c = 10335.57 ; ;

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

p = a+b+c = 23770.2+25920+10335.57 = 60025.77 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60025.77 }{ 2 } = 30012.88 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30012.88 * (30012.88-23770.2)(30012.88-25920)(30012.88-10335.57) } ; ; T = sqrt{ 1.509 * 10**{ 16 } } = 122839274.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 122839274.23 }{ 23770.2 } = 10335.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 122839274.23 }{ 25920 } = 9478.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 122839274.23 }{ 10335.57 } = 23770.2 ; ;

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{ 23770.2**2-25920**2-10335.57**2 }{ 2 * 25920 * 10335.57 } ) = 66° 30' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25920**2-23770.2**2-10335.57**2 }{ 2 * 23770.2 * 10335.57 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10335.57**2-23770.2**2-25920**2 }{ 2 * 25920 * 23770.2 } ) = 23° 30' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 122839274.23 }{ 30012.88 } = 4092.88 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23770.2 }{ 2 * sin 66° 30' } = 12960 ; ;




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