Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 17.2   b = 22.1   c = 34.41333219119

Area: T = 161.6211370198
Perimeter: p = 73.71333219119
Semiperimeter: s = 36.8576660956

Angle ∠ A = α = 25.15219629485° = 25°9'7″ = 0.43989845668 rad
Angle ∠ B = β = 33.1° = 33°6' = 0.57877039824 rad
Angle ∠ C = γ = 121.7488037052° = 121°44'53″ = 2.12549041044 rad

Height: ha = 18.79331825811
Height: hb = 14.62663683437
Height: hc = 9.39329537294

Median: ma = 27.61112904897
Median: mb = 24.85987180383
Median: mc = 9.80108070457

Inradius: r = 4.38551332705
Circumradius: R = 20.23443166457

Vertex coordinates: A[34.41333219119; 0] B[0; 0] C[14.40987619259; 9.39329537294]
Centroid: CG[16.27440279459; 3.13109845765]
Coordinates of the circumscribed circle: U[17.2076660956; -10.64769896621]
Coordinates of the inscribed circle: I[14.7576660956; 4.38551332705]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.8488037052° = 154°50'53″ = 0.43989845668 rad
∠ B' = β' = 146.9° = 146°54' = 0.57877039824 rad
∠ C' = γ' = 58.25219629485° = 58°15'7″ = 2.12549041044 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 17.2 ; ; b = 22.1 ; ; beta = 33° 6' ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 22.1**2 = 17.2**2 + c**2 -2 * 22.1 * c * cos (33° 6') ; ; ; ; c**2 -28.818c -192.57 =0 ; ; p=1; q=-28.8175238517; r=-192.57 ; ; D = q**2 - 4pr = 28.818**2 - 4 * 1 * (-192.57) = 1600.72968095 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 28.82 ± sqrt{ 1600.73 } }{ 2 } ; ; c_{1,2} = 14.4087619259 ± 20.0045599861 ; ;
c_{1} = 34.4133219119 ; ; c_{2} = -5.5957980602 ; ; ; ; (c -34.4133219119) (c +5.5957980602) = 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 = 17.2 ; ; b = 22.1 ; ; c = 34.41 ; ;

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

p = a+b+c = 17.2+22.1+34.41 = 73.71 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73.71 }{ 2 } = 36.86 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.86 * (36.86-17.2)(36.86-22.1)(36.86-34.41) } ; ; T = sqrt{ 26121.47 } = 161.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161.62 }{ 17.2 } = 18.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161.62 }{ 22.1 } = 14.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161.62 }{ 34.41 } = 9.39 ; ;

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{ 17.2**2-22.1**2-34.41**2 }{ 2 * 22.1 * 34.41 } ) = 25° 9'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22.1**2-17.2**2-34.41**2 }{ 2 * 17.2 * 34.41 } ) = 33° 6' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 34.41**2-17.2**2-22.1**2 }{ 2 * 22.1 * 17.2 } ) = 121° 44'53" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161.62 }{ 36.86 } = 4.39 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.2 }{ 2 * sin 25° 9'7" } = 20.23 ; ;




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