Triangle calculator SSA

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Triangle has two solutions with side c=36.43881226846 and with side c=3.87444476828

#1 Obtuse scalene triangle.

Sides: a = 22.24   b = 18.8   c = 36.43881226846

Area: T = 171.2421506699
Perimeter: p = 77.47881226846
Semiperimeter: s = 38.73990613423

Angle ∠ A = α = 29.99765870083° = 29°59'48″ = 0.52435392077 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 125.0033412992° = 125°12″ = 2.18217211329 rad

Height: ha = 15.39994160701
Height: hb = 18.21771815637
Height: hc = 9.39990301411

Median: ma = 26.77656230999
Median: mb = 28.68547902623
Median: mc = 9.59765933437

Inradius: r = 4.42203834777
Circumradius: R = 22.24222948816

Vertex coordinates: A[36.43881226846; 0] B[0; 0] C[20.15662851837; 9.39990301411]
Centroid: CG[18.86548026228; 3.1333010047]
Coordinates of the circumscribed circle: U[18.21990613423; -12.75987415291]
Coordinates of the inscribed circle: I[19.93990613423; 4.42203834777]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0033412992° = 150°12″ = 0.52435392077 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 54.99765870083° = 54°59'48″ = 2.18217211329 rad




How did we calculate this triangle?

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 = 22.24 ; ; b = 18.8 ; ; c = 36.44 ; ;

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

p = a+b+c = 22.24+18.8+36.44 = 77.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77.48 }{ 2 } = 38.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.74 * (38.74-22.24)(38.74-18.8)(38.74-36.44) } ; ; T = sqrt{ 29323.65 } = 171.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.24 }{ 22.24 } = 15.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.24 }{ 18.8 } = 18.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.24 }{ 36.44 } = 9.4 ; ;

5. 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{ 22.24**2-18.8**2-36.44**2 }{ 2 * 18.8 * 36.44 } ) = 29° 59'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18.8**2-22.24**2-36.44**2 }{ 2 * 22.24 * 36.44 } ) = 25° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 36.44**2-22.24**2-18.8**2 }{ 2 * 18.8 * 22.24 } ) = 125° 12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.24 }{ 38.74 } = 4.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22.24 }{ 2 * sin 29° 59'48" } = 22.24 ; ;





#2 Obtuse scalene triangle.

Sides: a = 22.24   b = 18.8   c = 3.87444476828

Area: T = 18.20880252753
Perimeter: p = 44.91444476828
Semiperimeter: s = 22.45772238414

Angle ∠ A = α = 150.0033412992° = 150°12″ = 2.61880534459 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 4.99765870083° = 4°59'48″ = 0.08772068947 rad

Height: ha = 1.63774123449
Height: hb = 1.93770239655
Height: hc = 9.39990301411

Median: ma = 7.78327548094
Median: mb = 12.90217236222
Median: mc = 20.50106332534

Inradius: r = 0.81107870057
Circumradius: R = 22.24222948816

Vertex coordinates: A[3.87444476828; 0] B[0; 0] C[20.15662851837; 9.39990301411]
Centroid: CG[8.01102442888; 3.1333010047]
Coordinates of the circumscribed circle: U[1.93772238414; 22.15877716702]
Coordinates of the inscribed circle: I[3.65772238414; 0.81107870057]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.99765870083° = 29°59'48″ = 2.61880534459 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 175.0033412992° = 175°12″ = 0.08772068947 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 22.24 ; ; b = 18.8 ; ; beta = 25° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 18.8**2 = 22.24**2 + c**2 -2 * 18.8 * c * cos (25° ) ; ; ; ; c**2 -40.313c +141.178 =0 ; ; p=1; q=-40.3125703674; r=141.1776 ; ; D = q**2 - 4pr = 40.313**2 - 4 * 1 * 141.178 = 1060.39292963 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 40.31 ± sqrt{ 1060.39 } }{ 2 } ; ; c_{1,2} = 20.1562851837 ± 16.2818375009 ; ;
c_{1} = 36.4381226846 ; ; c_{2} = 3.87444768277 ; ; ; ; (c -36.4381226846) (c -3.87444768277) = 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 = 22.24 ; ; b = 18.8 ; ; c = 3.87 ; ;

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

p = a+b+c = 22.24+18.8+3.87 = 44.91 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44.91 }{ 2 } = 22.46 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.46 * (22.46-22.24)(22.46-18.8)(22.46-3.87) } ; ; T = sqrt{ 331.53 } = 18.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.21 }{ 22.24 } = 1.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.21 }{ 18.8 } = 1.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.21 }{ 3.87 } = 9.4 ; ;

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{ 22.24**2-18.8**2-3.87**2 }{ 2 * 18.8 * 3.87 } ) = 150° 12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18.8**2-22.24**2-3.87**2 }{ 2 * 22.24 * 3.87 } ) = 25° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.87**2-22.24**2-18.8**2 }{ 2 * 18.8 * 22.24 } ) = 4° 59'48" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.21 }{ 22.46 } = 0.81 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22.24 }{ 2 * sin 150° 12" } = 22.24 ; ;




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