Triangle calculator SSA

Please enter two sides and a non-included angle
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Obtuse scalene triangle.

Sides: a = 200   b = 234   c = 71.00658387676

Area: T = 6672.366627227
Perimeter: p = 505.0065838768
Semiperimeter: s = 252.5032919384

Angle ∠ A = α = 53.43325521527° = 53°25'57″ = 0.93325739628 rad
Angle ∠ B = β = 110° = 1.92198621772 rad
Angle ∠ C = γ = 16.56774478473° = 16°34'3″ = 0.28991565136 rad

Height: ha = 66.72436627227
Height: hb = 57.02987715578
Height: hc = 187.9398524157

Median: ma = 141.0643512538
Median: mb = 93.97882664745
Median: mc = 214.7549953935

Inradius: r = 26.42549074369
Circumradius: R = 124.509879938

Vertex coordinates: A[71.00658387676; 0] B[0; 0] C[-68.40440286651; 187.9398524157]
Centroid: CG[0.86772700342; 62.64661747191]
Coordinates of the circumscribed circle: U[35.50329193838; 119.3439783133]
Coordinates of the inscribed circle: I[18.50329193838; 26.42549074369]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.5677447847° = 126°34'3″ = 0.93325739628 rad
∠ B' = β' = 70° = 1.92198621772 rad
∠ C' = γ' = 163.4332552153° = 163°25'57″ = 0.28991565136 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 200 ; ; b = 234 ; ; beta = 110° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 234**2 = 200**2 + c**2 -2 * 234 * c * cos (110° ) ; ; ; ; c**2 +136.808c -14756 =0 ; ; p=1; q=136.80805733; r=-14756 ; ; D = q**2 - 4pr = 136.808**2 - 4 * 1 * (-14756) = 77740.4445505 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ -136.81 ± sqrt{ 77740.44 } }{ 2 } ; ; c_{1,2} = -68.4040286651 ± 139.409867433 ; ;
c_{1} = 71.0058387676 ; ; c_{2} = -207.813896098 ; ; ; ; (c -71.0058387676) (c +207.813896098) = 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 = 200 ; ; b = 234 ; ; c = 71.01 ; ;

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

p = a+b+c = 200+234+71.01 = 505.01 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 505.01 }{ 2 } = 252.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 252.5 * (252.5-200)(252.5-234)(252.5-71.01) } ; ; T = sqrt{ 44520471.67 } = 6672.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6672.37 }{ 200 } = 66.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6672.37 }{ 234 } = 57.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6672.37 }{ 71.01 } = 187.94 ; ;

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{ 200**2-234**2-71.01**2 }{ 2 * 234 * 71.01 } ) = 53° 25'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 234**2-200**2-71.01**2 }{ 2 * 200 * 71.01 } ) = 110° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 71.01**2-200**2-234**2 }{ 2 * 234 * 200 } ) = 16° 34'3" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6672.37 }{ 252.5 } = 26.42 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 200 }{ 2 * sin 53° 25'57" } = 124.51 ; ;




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