Triangle calculator SSA

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Triangle has two solutions with side c=29.30217716025 and with side c=2.6610931259

#1 Obtuse scalene triangle.

Sides: a = 18.1   b = 15.8   c = 29.30217716025

Area: T = 124.4954953985
Perimeter: p = 63.20217716025
Semiperimeter: s = 31.60108858013

Angle ∠ A = α = 32.53548405162° = 32°32'5″ = 0.56878400886 rad
Angle ∠ B = β = 28° = 0.48986921906 rad
Angle ∠ C = γ = 119.4655159484° = 119°27'55″ = 2.08550603744 rad

Height: ha = 13.75663485066
Height: hb = 15.75988549348
Height: hc = 8.49774352864

Median: ma = 21.73304949213
Median: mb = 23.03767512797
Median: mc = 8.60109618787

Inradius: r = 3.94396033
Circumradius: R = 16.82774302987

Vertex coordinates: A[29.30217716025; 0] B[0; 0] C[15.98113514307; 8.49774352864]
Centroid: CG[15.09443743444; 2.83224784288]
Coordinates of the circumscribed circle: U[14.65108858013; -8.27773157301]
Coordinates of the inscribed circle: I[15.80108858013; 3.94396033]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.4655159484° = 147°27'55″ = 0.56878400886 rad
∠ B' = β' = 152° = 0.48986921906 rad
∠ C' = γ' = 60.53548405162° = 60°32'5″ = 2.08550603744 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 = 18.1 ; ; b = 15.8 ; ; c = 29.3 ; ;

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

p = a+b+c = 18.1+15.8+29.3 = 63.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63.2 }{ 2 } = 31.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.6 * (31.6-18.1)(31.6-15.8)(31.6-29.3) } ; ; T = sqrt{ 15498.99 } = 124.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.49 }{ 18.1 } = 13.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.49 }{ 15.8 } = 15.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.49 }{ 29.3 } = 8.5 ; ;

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{ 18.1**2-15.8**2-29.3**2 }{ 2 * 15.8 * 29.3 } ) = 32° 32'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.8**2-18.1**2-29.3**2 }{ 2 * 18.1 * 29.3 } ) = 28° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29.3**2-18.1**2-15.8**2 }{ 2 * 15.8 * 18.1 } ) = 119° 27'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.49 }{ 31.6 } = 3.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.1 }{ 2 * sin 32° 32'5" } = 16.83 ; ;





#2 Obtuse scalene triangle.

Sides: a = 18.1   b = 15.8   c = 2.6610931259

Area: T = 11.30655455873
Perimeter: p = 36.5610931259
Semiperimeter: s = 18.28804656295

Angle ∠ A = α = 147.4655159484° = 147°27'55″ = 2.5743752565 rad
Angle ∠ B = β = 28° = 0.48986921906 rad
Angle ∠ C = γ = 4.53548405162° = 4°32'5″ = 0.07991478981 rad

Height: ha = 1.24992315566
Height: hb = 1.43110817199
Height: hc = 8.49774352864

Median: ma = 6.81659942475
Median: mb = 10.24437921485
Median: mc = 16.93767901684

Inradius: r = 0.61884495415
Circumradius: R = 16.82774302987

Vertex coordinates: A[2.6610931259; 0] B[0; 0] C[15.98113514307; 8.49774352864]
Centroid: CG[6.21440942299; 2.83224784288]
Coordinates of the circumscribed circle: U[1.33304656295; 16.77547510165]
Coordinates of the inscribed circle: I[2.48804656295; 0.61884495415]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 32.53548405162° = 32°32'5″ = 2.5743752565 rad
∠ B' = β' = 152° = 0.48986921906 rad
∠ C' = γ' = 175.4655159484° = 175°27'55″ = 0.07991478981 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 18.1 ; ; b = 15.8 ; ; beta = 28° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 15.8**2 = 18.1**2 + c**2 -2 * 15.8 * c * cos (28° ) ; ; ; ; c**2 -31.963c +77.97 =0 ; ; p=1; q=-31.9627028615; r=77.97 ; ; D = q**2 - 4pr = 31.963**2 - 4 * 1 * 77.97 = 709.734374212 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 31.96 ± sqrt{ 709.73 } }{ 2 } ; ; c_{1,2} = 15.9813514307 ± 13.3204201718 ; ;
c_{1} = 29.3017716025 ; ; c_{2} = 2.66093125896 ; ; ; ; (c -29.3017716025) (c -2.66093125896) = 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 = 18.1 ; ; b = 15.8 ; ; c = 2.66 ; ;

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

p = a+b+c = 18.1+15.8+2.66 = 36.56 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36.56 }{ 2 } = 18.28 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.28 * (18.28-18.1)(18.28-15.8)(18.28-2.66) } ; ; T = sqrt{ 127.82 } = 11.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.31 }{ 18.1 } = 1.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.31 }{ 15.8 } = 1.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.31 }{ 2.66 } = 8.5 ; ;

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{ 18.1**2-15.8**2-2.66**2 }{ 2 * 15.8 * 2.66 } ) = 147° 27'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.8**2-18.1**2-2.66**2 }{ 2 * 18.1 * 2.66 } ) = 28° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.66**2-18.1**2-15.8**2 }{ 2 * 15.8 * 18.1 } ) = 4° 32'5" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.31 }{ 18.28 } = 0.62 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.1 }{ 2 * sin 147° 27'55" } = 16.83 ; ;




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