Triangle calculator SSA

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Triangle has two solutions with side c=9.93298460877 and with side c=1.64765512009

#1 Obtuse scalene triangle.

Sides: a = 6.2   b = 4.7   c = 9.93298460877

Area: T = 11.03114696034
Perimeter: p = 20.83298460877
Semiperimeter: s = 10.41549230439

Angle ∠ A = α = 28.21223488407° = 28°12'44″ = 0.4922398377 rad
Angle ∠ B = β = 21° = 0.36765191429 rad
Angle ∠ C = γ = 130.7887651159° = 130°47'16″ = 2.28326751337 rad

Height: ha = 3.55985385818
Height: hb = 4.69442423844
Height: hc = 2.22218812872

Median: ma = 7.12329152503
Median: mb = 7.93771545067
Median: mc = 2.3769501882

Inradius: r = 1.05991983788
Circumradius: R = 6.55875060576

Vertex coordinates: A[9.93298460877; 0] B[0; 0] C[5.78881986443; 2.22218812872]
Centroid: CG[5.2399348244; 0.74106270957]
Coordinates of the circumscribed circle: U[4.96549230439; -4.28437395888]
Coordinates of the inscribed circle: I[5.71549230439; 1.05991983788]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.7887651159° = 151°47'16″ = 0.4922398377 rad
∠ B' = β' = 159° = 0.36765191429 rad
∠ C' = γ' = 49.21223488407° = 49°12'44″ = 2.28326751337 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 = 6.2 ; ; b = 4.7 ; ; c = 9.93 ; ;

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

p = a+b+c = 6.2+4.7+9.93 = 20.83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.83 }{ 2 } = 10.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.41 * (10.41-6.2)(10.41-4.7)(10.41-9.93) } ; ; T = sqrt{ 121.69 } = 11.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.03 }{ 6.2 } = 3.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.03 }{ 4.7 } = 4.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.03 }{ 9.93 } = 2.22 ; ;

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{ 6.2**2-4.7**2-9.93**2 }{ 2 * 4.7 * 9.93 } ) = 28° 12'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.7**2-6.2**2-9.93**2 }{ 2 * 6.2 * 9.93 } ) = 21° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.93**2-6.2**2-4.7**2 }{ 2 * 4.7 * 6.2 } ) = 130° 47'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.03 }{ 10.41 } = 1.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.2 }{ 2 * sin 28° 12'44" } = 6.56 ; ;





#2 Obtuse scalene triangle.

Sides: a = 6.2   b = 4.7   c = 1.64765512009

Area: T = 1.82992206508
Perimeter: p = 12.54765512009
Semiperimeter: s = 6.27332756004

Angle ∠ A = α = 151.7887651159° = 151°47'16″ = 2.64991942766 rad
Angle ∠ B = β = 21° = 0.36765191429 rad
Angle ∠ C = γ = 7.21223488407° = 7°12'44″ = 0.12658792341 rad

Height: ha = 0.59900711777
Height: hb = 0.77883917663
Height: hc = 2.22218812872

Median: ma = 1.67704985569
Median: mb = 3.88798280153
Median: mc = 5.43994133218

Inradius: r = 0.29215893972
Circumradius: R = 6.55875060576

Vertex coordinates: A[1.64765512009; 0] B[0; 0] C[5.78881986443; 2.22218812872]
Centroid: CG[2.47882499484; 0.74106270957]
Coordinates of the circumscribed circle: U[0.82332756004; 6.50656208759]
Coordinates of the inscribed circle: I[1.57332756004; 0.29215893972]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 28.21223488407° = 28°12'44″ = 2.64991942766 rad
∠ B' = β' = 159° = 0.36765191429 rad
∠ C' = γ' = 172.7887651159° = 172°47'16″ = 0.12658792341 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 6.2 ; ; b = 4.7 ; ; beta = 21° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 4.7**2 = 6.2**2 + c**2 -2 * 4.7 * c * cos (21° ) ; ; ; ; c**2 -11.576c +16.35 =0 ; ; p=1; q=-11.5763972886; r=16.35 ; ; D = q**2 - 4pr = 11.576**2 - 4 * 1 * 16.35 = 68.6129741827 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 11.58 ± sqrt{ 68.61 } }{ 2 } ; ; c_{1,2} = 5.78819864428 ± 4.14164744343 ; ; c_{1} = 9.92984608771 ; ;
c_{2} = 1.64655120085 ; ; ; ; (c -9.92984608771) (c -1.64655120085) = 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 = 6.2 ; ; b = 4.7 ; ; c = 1.65 ; ;

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

p = a+b+c = 6.2+4.7+1.65 = 12.55 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.55 }{ 2 } = 6.27 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.27 * (6.27-6.2)(6.27-4.7)(6.27-1.65) } ; ; T = sqrt{ 3.35 } = 1.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.83 }{ 6.2 } = 0.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.83 }{ 4.7 } = 0.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.83 }{ 1.65 } = 2.22 ; ;

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{ 6.2**2-4.7**2-1.65**2 }{ 2 * 4.7 * 1.65 } ) = 151° 47'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.7**2-6.2**2-1.65**2 }{ 2 * 6.2 * 1.65 } ) = 21° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.65**2-6.2**2-4.7**2 }{ 2 * 4.7 * 6.2 } ) = 7° 12'44" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.83 }{ 6.27 } = 0.29 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.2 }{ 2 * sin 151° 47'16" } = 6.56 ; ;




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