Triangle calculator SSA

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Triangle has two solutions with side c=28.65444440559 and with side c=4.58774210557

#1 Acute scalene triangle.

Sides: a = 60.3   b = 59.2   c = 28.65444440559

Area: T = 830.4644247603
Perimeter: p = 148.1544444056
Semiperimeter: s = 74.07772220279

Angle ∠ A = α = 78.27218264562° = 78°16'19″ = 1.36661010832 rad
Angle ∠ B = β = 74° = 1.29215436465 rad
Angle ∠ C = γ = 27.72881735438° = 27°43'41″ = 0.48439479239 rad

Height: ha = 27.54444194893
Height: hb = 28.05662245812
Height: hc = 57.96440802651

Median: ma = 35.41095478943
Median: mb = 36.77553121275
Median: mc = 58.00994449979

Inradius: r = 11.21107909134
Circumradius: R = 30.79328633015

Vertex coordinates: A[28.65444440559; 0] B[0; 0] C[16.62109325558; 57.96440802651]
Centroid: CG[15.09217922039; 19.32113600884]
Coordinates of the circumscribed circle: U[14.32772220279; 27.2576763184]
Coordinates of the inscribed circle: I[14.87772220279; 11.21107909134]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.7288173544° = 101°43'41″ = 1.36661010832 rad
∠ B' = β' = 106° = 1.29215436465 rad
∠ C' = γ' = 152.2721826456° = 152°16'19″ = 0.48439479239 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 = 60.3 ; ; b = 59.2 ; ; c = 28.65 ; ;

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

p = a+b+c = 60.3+59.2+28.65 = 148.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 148.15 }{ 2 } = 74.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 74.08 * (74.08-60.3)(74.08-59.2)(74.08-28.65) } ; ; T = sqrt{ 689670.87 } = 830.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 830.46 }{ 60.3 } = 27.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 830.46 }{ 59.2 } = 28.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 830.46 }{ 28.65 } = 57.96 ; ;

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{ 60.3**2-59.2**2-28.65**2 }{ 2 * 59.2 * 28.65 } ) = 78° 16'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 59.2**2-60.3**2-28.65**2 }{ 2 * 60.3 * 28.65 } ) = 74° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28.65**2-60.3**2-59.2**2 }{ 2 * 59.2 * 60.3 } ) = 27° 43'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 830.46 }{ 74.08 } = 11.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 60.3 }{ 2 * sin 78° 16'19" } = 30.79 ; ;





#2 Obtuse scalene triangle.

Sides: a = 60.3   b = 59.2   c = 4.58774210557

Area: T = 132.953282114
Perimeter: p = 124.0877421056
Semiperimeter: s = 62.04437105278

Angle ∠ A = α = 101.7288173544° = 101°43'41″ = 1.77554915704 rad
Angle ∠ B = β = 74° = 1.29215436465 rad
Angle ∠ C = γ = 4.27218264562° = 4°16'19″ = 0.07545574367 rad

Height: ha = 4.41097121439
Height: hb = 4.49216493628
Height: hc = 57.96440802651

Median: ma = 29.22201936334
Median: mb = 30.86110955083
Median: mc = 59.70884909541

Inradius: r = 2.14328895856
Circumradius: R = 30.79328633015

Vertex coordinates: A[4.58774210557; 0] B[0; 0] C[16.62109325558; 57.96440802651]
Centroid: CG[7.06994512038; 19.32113600884]
Coordinates of the circumscribed circle: U[2.29437105278; 30.70773170811]
Coordinates of the inscribed circle: I[2.84437105278; 2.14328895856]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 78.27218264562° = 78°16'19″ = 1.77554915704 rad
∠ B' = β' = 106° = 1.29215436465 rad
∠ C' = γ' = 175.7288173544° = 175°43'41″ = 0.07545574367 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 60.3 ; ; b = 59.2 ; ; beta = 74° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 59.2**2 = 60.3**2 + c**2 -2 * 59.2 * c * cos (74° ) ; ; ; ; c**2 -33.242c +131.45 =0 ; ; p=1; q=-33.2418651115; r=131.45 ; ; D = q**2 - 4pr = 33.242**2 - 4 * 1 * 131.45 = 579.221596093 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 33.24 ± sqrt{ 579.22 } }{ 2 } ; ; c_{1,2} = 16.6209325558 ± 12.0335115001 ; ;
c_{1} = 28.6544440559 ; ; c_{2} = 4.58742105565 ; ; ; ; (c -28.6544440559) (c -4.58742105565) = 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 = 60.3 ; ; b = 59.2 ; ; c = 4.59 ; ;

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

p = a+b+c = 60.3+59.2+4.59 = 124.09 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 124.09 }{ 2 } = 62.04 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 62.04 * (62.04-60.3)(62.04-59.2)(62.04-4.59) } ; ; T = sqrt{ 17676.45 } = 132.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 132.95 }{ 60.3 } = 4.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 132.95 }{ 59.2 } = 4.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 132.95 }{ 4.59 } = 57.96 ; ;

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{ 60.3**2-59.2**2-4.59**2 }{ 2 * 59.2 * 4.59 } ) = 101° 43'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 59.2**2-60.3**2-4.59**2 }{ 2 * 60.3 * 4.59 } ) = 74° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.59**2-60.3**2-59.2**2 }{ 2 * 59.2 * 60.3 } ) = 4° 16'19" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 132.95 }{ 62.04 } = 2.14 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 60.3 }{ 2 * sin 101° 43'41" } = 30.79 ; ;




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