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?

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 ; ;

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

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

2. Semiperimeter of the triangle

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

3. 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 ; ;

4. 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 ; ;

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{ 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" ; ;

6. Inradius

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

7. 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 - 2bc cos( beta ) ; ; 32.7**2 = 43**2 + c**2 -2 * 32.7 * c * cos (40° 48') ; ; ; ; c**2 -65.102c +779.71 =0 ; ; p=1; q=-65.1015747861; 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} = 32.550787393 ± 16.7285313135 ; ;
c_{1} = 49.2793187065 ; ; c_{2} = 15.8222560795 ; ; ; ; (c -49.2793187065) (c -15.8222560795) = 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 = 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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