Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 33   b = 50   c = 21.49114366531

Area: T = 263.5265624023
Perimeter: p = 104.4911436653
Semiperimeter: s = 52.24657183265

Angle ∠ A = α = 29.37218451774° = 29°22'19″ = 0.51326354057 rad
Angle ∠ B = β = 132° = 2.30438346126 rad
Angle ∠ C = γ = 18.62881548226° = 18°37'41″ = 0.32551226352 rad

Height: ha = 15.97112499408
Height: hb = 10.54110249609
Height: hc = 24.52437792408

Median: ma = 34.76662325354
Median: mb = 12.26554361809
Median: mc = 40.97659629252

Inradius: r = 5.04439659452
Circumradius: R = 33.64108182402

Vertex coordinates: A[21.49114366531; 0] B[0; 0] C[-22.08113100098; 24.52437792408]
Centroid: CG[-0.19766244523; 8.17545930803]
Coordinates of the circumscribed circle: U[10.74657183265; 31.87884282786]
Coordinates of the inscribed circle: I[2.24657183265; 5.04439659452]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.6288154823° = 150°37'41″ = 0.51326354057 rad
∠ B' = β' = 48° = 2.30438346126 rad
∠ C' = γ' = 161.3721845177° = 161°22'19″ = 0.32551226352 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 33 ; ; b = 50 ; ; beta = 132° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 50**2 = 33**2 + c**2 -2 * 50 * c * cos (132° ) ; ; ; ; c**2 +44.163c -1411 =0 ; ; p=1; q=44.1626200197; r=-1411 ; ; D = q**2 - 4pr = 44.163**2 - 4 * 1 * (-1411) = 7594.337007 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ -44.16 ± sqrt{ 7594.34 } }{ 2 } ; ; c_{1,2} = -22.0813100098 ± 43.5727466629 ; ; c_{1} = 21.4914366531 ; ;
c_{2} = -65.6540566728 ; ; ; ; (c -21.4914366531) (c +65.6540566728) = 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 = 33 ; ; b = 50 ; ; c = 21.49 ; ;

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

p = a+b+c = 33+50+21.49 = 104.49 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 104.49 }{ 2 } = 52.25 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52.25 * (52.25-33)(52.25-50)(52.25-21.49) } ; ; T = sqrt{ 69445.75 } = 263.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 263.53 }{ 33 } = 15.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 263.53 }{ 50 } = 10.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 263.53 }{ 21.49 } = 24.52 ; ;

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{ 33**2-50**2-21.49**2 }{ 2 * 50 * 21.49 } ) = 29° 22'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 50**2-33**2-21.49**2 }{ 2 * 33 * 21.49 } ) = 132° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21.49**2-33**2-50**2 }{ 2 * 50 * 33 } ) = 18° 37'41" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 263.53 }{ 52.25 } = 5.04 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 33 }{ 2 * sin 29° 22'19" } = 33.64 ; ;




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