Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 0.6133248   b = 20.9165512   c = 20.895509981

Area: T = 6.4065827473
Perimeter: p = 42.424385981
Semiperimeter: s = 21.2121929905

Angle ∠ A = α = 1.68798756654° = 1°40'48″ = 0.02993193614 rad
Angle ∠ B = β = 91.0677321° = 91°4'2″ = 1.58994245924 rad
Angle ∠ C = γ = 87.25328033346° = 87°15'10″ = 1.52328486998 rad

Height: ha = 20.89114744867
Height: hb = 0.61325432141
Height: hc = 0.61331416008

Median: ma = 20.90330596054
Median: mb = 10.44663378288
Median: mc = 10.47769298293

Inradius: r = 0.3021991733
Circumradius: R = 10.46595707473

Vertex coordinates: A[20.895509981; 0] B[0; 0] C[-0.0111423086; 0.61331416008]
Centroid: CG[6.96112255747; 0.20443805336]
Coordinates of the circumscribed circle: U[10.4487549905; 0.50113194585]
Coordinates of the inscribed circle: I[0.2966417905; 0.3021991733]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178.3220124335° = 178°19'12″ = 0.02993193614 rad
∠ B' = β' = 88.9332679° = 88°55'58″ = 1.58994245924 rad
∠ C' = γ' = 92.74771966654° = 92°44'50″ = 1.52328486998 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 0.61 ; ; b = 20.92 ; ; beta = 91° 4'2" ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 20.92**2 = 0.61**2 + c**2 -2 * 20.92 * c * cos (91° 4'2") ; ; ; ; c**2 +0.023c -437.083 =0 ; ; p=1; q=0.0228461719063; r=-437.082569113 ; ; D = q**2 - 4pr = 0.023**2 - 4 * 1 * (-437.083) = 1748.3307984 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ -0.02 ± sqrt{ 1748.33 } }{ 2 } ; ; c_{1,2} = -0.0114230859532 ± 20.906522896 ; ;
c_{1} = 20.89509981 ; ; c_{2} = -20.9179459819 ; ; ; ; (c -20.89509981) (c +20.9179459819) = 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 = 0.61 ; ; b = 20.92 ; ; c = 20.9 ; ;

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

p = a+b+c = 0.61+20.92+20.9 = 42.42 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42.42 }{ 2 } = 21.21 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.21 * (21.21-0.61)(21.21-20.92)(21.21-20.9) } ; ; T = sqrt{ 41.03 } = 6.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.41 }{ 0.61 } = 20.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.41 }{ 20.92 } = 0.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.41 }{ 20.9 } = 0.61 ; ;

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{ 0.61**2-20.92**2-20.9**2 }{ 2 * 20.92 * 20.9 } ) = 1° 40'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20.92**2-0.61**2-20.9**2 }{ 2 * 0.61 * 20.9 } ) = 91° 4'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20.9**2-0.61**2-20.92**2 }{ 2 * 20.92 * 0.61 } ) = 87° 15'10" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.41 }{ 21.21 } = 0.3 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.61 }{ 2 * sin 1° 40'48" } = 10.46 ; ;




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