Triangle calculator SSA

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Triangle has two solutions with side c=37.41656605978 and with side c=25.57875251515

#1 Acute scalene triangle.

Sides: a = 49   b = 38   c = 37.41656605978

Area: T = 702.222044272
Perimeter: p = 124.4165660598
Semiperimeter: s = 62.20878302989

Angle ∠ A = α = 81.03988370467° = 81°2'20″ = 1.41443945285 rad
Angle ∠ B = β = 50° = 0.8732664626 rad
Angle ∠ C = γ = 48.96111629533° = 48°57'40″ = 0.85545334991 rad

Height: ha = 28.66220588865
Height: hb = 36.95989706695
Height: hc = 37.53661777128

Median: ma = 28.66655861441
Median: mb = 39.23660271814
Median: mc = 39.65549755454

Inradius: r = 11.28882966557
Circumradius: R = 24.80327384973

Vertex coordinates: A[37.41656605978; 0] B[0; 0] C[31.49765928746; 37.53661777128]
Centroid: CG[22.97107511575; 12.51220592376]
Coordinates of the circumscribed circle: U[18.70878302989; 16.28547450847]
Coordinates of the inscribed circle: I[24.20878302989; 11.28882966557]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.96111629533° = 98°57'40″ = 1.41443945285 rad
∠ B' = β' = 130° = 0.8732664626 rad
∠ C' = γ' = 131.0398837047° = 131°2'20″ = 0.85545334991 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 = 49 ; ; b = 38 ; ; c = 37.42 ; ;

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

p = a+b+c = 49+38+37.42 = 124.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 124.42 }{ 2 } = 62.21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 62.21 * (62.21-49)(62.21-38)(62.21-37.42) } ; ; T = sqrt{ 493113.55 } = 702.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 702.22 }{ 49 } = 28.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 702.22 }{ 38 } = 36.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 702.22 }{ 37.42 } = 37.54 ; ;

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{ 49**2-38**2-37.42**2 }{ 2 * 38 * 37.42 } ) = 81° 2'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 38**2-49**2-37.42**2 }{ 2 * 49 * 37.42 } ) = 50° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 37.42**2-49**2-38**2 }{ 2 * 38 * 49 } ) = 48° 57'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 702.22 }{ 62.21 } = 11.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 49 }{ 2 * sin 81° 2'20" } = 24.8 ; ;





#2 Obtuse scalene triangle.

Sides: a = 49   b = 38   c = 25.57875251515

Area: T = 480.0411264771
Perimeter: p = 112.5787525151
Semiperimeter: s = 56.28987625758

Angle ∠ A = α = 98.96111629533° = 98°57'40″ = 1.72771981251 rad
Angle ∠ B = β = 50° = 0.8732664626 rad
Angle ∠ C = γ = 31.03988370467° = 31°2'20″ = 0.54217299025 rad

Height: ha = 19.59435210111
Height: hb = 25.26553297248
Height: hc = 37.53661777128

Median: ma = 21.18661958935
Median: mb = 34.15655983177
Median: mc = 41.9439808676

Inradius: r = 8.52881900473
Circumradius: R = 24.80327384973

Vertex coordinates: A[25.57875251515; 0] B[0; 0] C[31.49765928746; 37.53661777128]
Centroid: CG[19.02547060087; 12.51220592376]
Coordinates of the circumscribed circle: U[12.78987625758; 21.25114326281]
Coordinates of the inscribed circle: I[18.28987625758; 8.52881900473]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 81.03988370467° = 81°2'20″ = 1.72771981251 rad
∠ B' = β' = 130° = 0.8732664626 rad
∠ C' = γ' = 148.9611162953° = 148°57'40″ = 0.54217299025 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 49 ; ; b = 38 ; ; beta = 50° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 38**2 = 49**2 + c**2 -2 * 38 * c * cos (50° ) ; ; ; ; c**2 -62.993c +957 =0 ; ; p=1; q=-62.9931857493; r=957 ; ; D = q**2 - 4pr = 62.993**2 - 4 * 1 * 957 = 140.141450843 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 62.99 ± sqrt{ 140.14 } }{ 2 } ; ; c_{1,2} = 31.4965928746 ± 5.91906772312 ; ; c_{1} = 37.4156605978 ; ;
c_{2} = 25.5775251515 ; ; ; ; (c -37.4156605978) (c -25.5775251515) = 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 = 49 ; ; b = 38 ; ; c = 25.58 ; ;

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

p = a+b+c = 49+38+25.58 = 112.58 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 112.58 }{ 2 } = 56.29 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 56.29 * (56.29-49)(56.29-38)(56.29-25.58) } ; ; T = sqrt{ 230439.62 } = 480.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 480.04 }{ 49 } = 19.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 480.04 }{ 38 } = 25.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 480.04 }{ 25.58 } = 37.54 ; ;

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{ 49**2-38**2-25.58**2 }{ 2 * 38 * 25.58 } ) = 98° 57'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 38**2-49**2-25.58**2 }{ 2 * 49 * 25.58 } ) = 50° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25.58**2-49**2-38**2 }{ 2 * 38 * 49 } ) = 31° 2'20" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 480.04 }{ 56.29 } = 8.53 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 49 }{ 2 * sin 98° 57'40" } = 24.8 ; ;




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