Triangle calculator SSA

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Triangle has two solutions with side c=49.27993187065 and with side c=15.82222560795

#1 Acute scalene triangle.

Sides: a = 43   b = 32.7   c = 49.27993187065

Area: T = 692.3032627159
Perimeter: p = 124.9799318706
Semiperimeter: s = 62.49896593533

Angle ∠ A = α = 59.23111444849° = 59°13'52″ = 1.0343778491 rad
Angle ∠ B = β = 40.8° = 40°48' = 0.71220943348 rad
Angle ∠ C = γ = 79.96988555151° = 79°58'8″ = 1.39657198278 rad

Height: ha = 32.22001221934
Height: hb = 42.34326683277
Height: hc = 28.09770859716

Median: ma = 35.86994943662
Median: mb = 43.26597171291
Median: mc = 29.19895903869

Inradius: r = 11.07986750052
Circumradius: R = 25.02221678046

Vertex coordinates: A[49.27993187065; 0] B[0; 0] C[32.5510787393; 28.09770859716]
Centroid: CG[27.27767020332; 9.36656953239]
Coordinates of the circumscribed circle: U[24.64396593533; 4.35884479572]
Coordinates of the inscribed circle: I[29.79896593533; 11.07986750052]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.7698855515° = 120°46'8″ = 1.0343778491 rad
∠ B' = β' = 139.2° = 139°12' = 0.71220943348 rad
∠ C' = γ' = 100.0311144485° = 100°1'52″ = 1.39657198278 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 43 ; ; b = 32.7 ; ; beta = 40° 48' ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 32.7**2 = 43**2 + c**2 -2 * 43 * c * cos (40° 48') ; ; ; ; c**2 -65.102c +779.71 =0 ; ; p=1; q=-65.102; r=779.71 ; ; D = q**2 - 4pr = 65.102**2 - 4 * 1 * 779.71 = 1119.37503962 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 65.1 ± sqrt{ 1119.38 } }{ 2 } ; ; c_{1,2} = 32.55078739 ± 16.7285313135 ; ; c_{1} = 49.2793187035 ; ;
c_{2} = 15.8222560765 ; ; ; ; (c -49.2793187035) (c -15.8222560765) = 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 = 43 ; ; b = 32.7 ; ; c = 49.28 ; ;

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

p = a+b+c = 43+32.7+49.28 = 124.98 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 124.98 }{ 2 } = 62.49 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 62.49 * (62.49-43)(62.49-32.7)(62.49-49.28) } ; ; T = sqrt{ 479282.93 } = 692.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 692.3 }{ 43 } = 32.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 692.3 }{ 32.7 } = 42.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 692.3 }{ 49.28 } = 28.1 ; ;

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{ 43**2-32.7**2-49.28**2 }{ 2 * 32.7 * 49.28 } ) = 59° 13'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 32.7**2-43**2-49.28**2 }{ 2 * 43 * 49.28 } ) = 40° 48' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 49.28**2-43**2-32.7**2 }{ 2 * 32.7 * 43 } ) = 79° 58'8" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 692.3 }{ 62.49 } = 11.08 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 43 }{ 2 * sin 59° 13'52" } = 25.02 ; ;





#2 Obtuse scalene triangle.

Sides: a = 43   b = 32.7   c = 15.82222560795

Area: T = 222.2879644666
Perimeter: p = 91.52222560795
Semiperimeter: s = 45.76111280398

Angle ∠ A = α = 120.7698855515° = 120°46'8″ = 2.10878141626 rad
Angle ∠ B = β = 40.8° = 40°48' = 0.71220943348 rad
Angle ∠ C = γ = 18.43111444849° = 18°25'52″ = 0.32216841562 rad

Height: ha = 10.3398588124
Height: hb = 13.59550853007
Height: hc = 28.09770859716

Median: ma = 14.05658490929
Median: mb = 27.97105093576
Median: mc = 37.37105639928

Inradius: r = 4.85773899768
Circumradius: R = 25.02221678046

Vertex coordinates: A[15.82222560795; 0] B[0; 0] C[32.5510787393; 28.09770859716]
Centroid: CG[16.12443478242; 9.36656953239]
Coordinates of the circumscribed circle: U[7.91111280398; 23.73986380144]
Coordinates of the inscribed circle: I[13.06111280398; 4.85773899768]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 59.23111444849° = 59°13'52″ = 2.10878141626 rad
∠ B' = β' = 139.2° = 139°12' = 0.71220943348 rad
∠ C' = γ' = 161.5698855515° = 161°34'8″ = 0.32216841562 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 43 ; ; b = 32.7 ; ; beta = 40° 48' ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 32.7**2 = 43**2 + c**2 -2 * 43 * c * cos (40° 48') ; ; ; ; c**2 -65.102c +779.71 =0 ; ; p=1; q=-65.102; r=779.71 ; ; D = q**2 - 4pr = 65.102**2 - 4 * 1 * 779.71 = 1119.37503962 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 65.1 ± sqrt{ 1119.38 } }{ 2 } ; ; c_{1,2} = 32.55078739 ± 16.7285313135 ; ; c_{1} = 49.2793187035 ; ; : Nr. 1
c_{2} = 15.8222560765 ; ; ; ; (c -49.2793187035) (c -15.8222560765) = 0 ; ; ; ; c>0 ; ; : Nr. 1


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 = 43 ; ; b = 32.7 ; ; c = 15.82 ; ;

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

p = a+b+c = 43+32.7+15.82 = 91.52 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 91.52 }{ 2 } = 45.76 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45.76 * (45.76-43)(45.76-32.7)(45.76-15.82) } ; ; T = sqrt{ 49408.24 } = 222.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 222.28 }{ 43 } = 10.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 222.28 }{ 32.7 } = 13.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 222.28 }{ 15.82 } = 28.1 ; ;

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{ 43**2-32.7**2-15.82**2 }{ 2 * 32.7 * 15.82 } ) = 120° 46'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 32.7**2-43**2-15.82**2 }{ 2 * 43 * 15.82 } ) = 40° 48' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15.82**2-43**2-32.7**2 }{ 2 * 32.7 * 43 } ) = 18° 25'52" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 222.28 }{ 45.76 } = 4.86 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 43 }{ 2 * sin 120° 46'8" } = 25.02 ; ;




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