Triangle calculator SSA

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Triangle has two solutions with side c=321.4222498361 and with side c=7.47699189143

#1 Obtuse scalene triangle.

Sides: a = 175   b = 168   c = 321.4222498361

Area: T = 9619.135478378
Perimeter: p = 664.4222498361
Semiperimeter: s = 332.211124918

Angle ∠ A = α = 20.87113600892° = 20°52'17″ = 0.36442739529 rad
Angle ∠ B = β = 20° = 0.34990658504 rad
Angle ∠ C = γ = 139.1298639911° = 139°7'43″ = 2.42882528503 rad

Height: ha = 109.9332968957
Height: hb = 114.5143509331
Height: hc = 59.8543525082

Median: ma = 241.0644226351
Median: mb = 244.7710731964
Median: mc = 59.97699456969

Inradius: r = 28.95548737663
Circumradius: R = 245.6599569614

Vertex coordinates: A[321.4222498361; 0] B[0; 0] C[164.4466208638; 59.8543525082]
Centroid: CG[161.9566235666; 19.95111750273]
Coordinates of the circumscribed circle: U[160.711124918; -185.7187643161]
Coordinates of the inscribed circle: I[164.211124918; 28.95548737663]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.1298639911° = 159°7'43″ = 0.36442739529 rad
∠ B' = β' = 160° = 0.34990658504 rad
∠ C' = γ' = 40.87113600892° = 40°52'17″ = 2.42882528503 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 = 175 ; ; b = 168 ; ; c = 321.42 ; ;

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

p = a+b+c = 175+168+321.42 = 664.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 664.42 }{ 2 } = 332.21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 332.21 * (332.21-175)(332.21-168)(332.21-321.42) } ; ; T = sqrt{ 92527753.99 } = 9619.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9619.13 }{ 175 } = 109.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9619.13 }{ 168 } = 114.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9619.13 }{ 321.42 } = 59.85 ; ;

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{ 175**2-168**2-321.42**2 }{ 2 * 168 * 321.42 } ) = 20° 52'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 168**2-175**2-321.42**2 }{ 2 * 175 * 321.42 } ) = 20° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 321.42**2-175**2-168**2 }{ 2 * 168 * 175 } ) = 139° 7'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9619.13 }{ 332.21 } = 28.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 175 }{ 2 * sin 20° 52'17" } = 245.6 ; ;





#2 Obtuse scalene triangle.

Sides: a = 175   b = 168   c = 7.47699189143

Area: T = 223.555048955
Perimeter: p = 350.4769918914
Semiperimeter: s = 175.2354959457

Angle ∠ A = α = 159.1298639911° = 159°7'43″ = 2.77773187007 rad
Angle ∠ B = β = 20° = 0.34990658504 rad
Angle ∠ C = γ = 0.87113600892° = 0°52'17″ = 0.01552081025 rad

Height: ha = 2.55548627377
Height: hb = 2.66113153518
Height: hc = 59.8543525082

Median: ma = 80.52111142763
Median: mb = 91.01986785462
Median: mc = 171.4955043887

Inradius: r = 1.27657185566
Circumradius: R = 245.6599569614

Vertex coordinates: A[7.47699189143; 0] B[0; 0] C[164.4466208638; 59.8543525082]
Centroid: CG[57.30553758506; 19.95111750273]
Coordinates of the circumscribed circle: U[3.73549594572; 245.5711168243]
Coordinates of the inscribed circle: I[7.23549594572; 1.27657185566]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 20.87113600892° = 20°52'17″ = 2.77773187007 rad
∠ B' = β' = 160° = 0.34990658504 rad
∠ C' = γ' = 179.1298639911° = 179°7'43″ = 0.01552081025 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 175 ; ; b = 168 ; ; beta = 20° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 168**2 = 175**2 + c**2 -2 * 168 * c * cos (20° ) ; ; ; ; c**2 -328.892c +2401 =0 ; ; p=1; q=-328.892417275; r=2401 ; ; D = q**2 - 4pr = 328.892**2 - 4 * 1 * 2401 = 98566.222141 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 328.89 ± sqrt{ 98566.22 } }{ 2 } ; ; c_{1,2} = 164.446208638 ± 156.976289723 ; ;
c_{1} = 321.422498361 ; ; c_{2} = 7.46991891434 ; ; ; ; (c -321.422498361) (c -7.46991891434) = 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 = 175 ; ; b = 168 ; ; c = 7.47 ; ;

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

p = a+b+c = 175+168+7.47 = 350.47 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 350.47 }{ 2 } = 175.23 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 175.23 * (175.23-175)(175.23-168)(175.23-7.47) } ; ; T = sqrt{ 49974.82 } = 223.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 223.55 }{ 175 } = 2.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 223.55 }{ 168 } = 2.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 223.55 }{ 7.47 } = 59.85 ; ;

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{ 175**2-168**2-7.47**2 }{ 2 * 168 * 7.47 } ) = 159° 7'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 168**2-175**2-7.47**2 }{ 2 * 175 * 7.47 } ) = 20° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.47**2-175**2-168**2 }{ 2 * 168 * 175 } ) = 0° 52'17" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 223.55 }{ 175.23 } = 1.28 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 175 }{ 2 * sin 159° 7'43" } = 245.6 ; ;




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