Triangle calculator SSA

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Triangle has two solutions with side c=28.0543789651 and with side c=2.03215579716

#1 Obtuse scalene triangle.

Sides: a = 15.73   b = 13.8   c = 28.0543789651

Area: T = 64.51097863024
Perimeter: p = 57.5843789651
Semiperimeter: s = 28.79218948255

Angle ∠ A = α = 19.46768474254° = 19°28'1″ = 0.34397605826 rad
Angle ∠ B = β = 17° = 0.29767059728 rad
Angle ∠ C = γ = 143.5333152575° = 143°31'59″ = 2.50551260982 rad

Height: ha = 8.20221343042
Height: hb = 9.34992443917
Height: hc = 4.59990069153

Median: ma = 20.66108163413
Median: mb = 21.67105792929
Median: mc = 4.7109848358

Inradius: r = 2.24105536938
Circumradius: R = 23.66000949768

Vertex coordinates: A[28.0543789651; 0] B[0; 0] C[15.04326738113; 4.59990069153]
Centroid: CG[14.36554878208; 1.53330023051]
Coordinates of the circumscribed circle: U[14.02768948255; -18.97992176991]
Coordinates of the inscribed circle: I[14.99218948255; 2.24105536938]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.5333152575° = 160°31'59″ = 0.34397605826 rad
∠ B' = β' = 163° = 0.29767059728 rad
∠ C' = γ' = 36.46768474254° = 36°28'1″ = 2.50551260982 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 = 15.73 ; ; b = 13.8 ; ; c = 28.05 ; ;

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

p = a+b+c = 15.73+13.8+28.05 = 57.58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57.58 }{ 2 } = 28.79 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.79 * (28.79-15.73)(28.79-13.8)(28.79-28.05) } ; ; T = sqrt{ 4161.51 } = 64.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.51 }{ 15.73 } = 8.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.51 }{ 13.8 } = 9.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.51 }{ 28.05 } = 4.6 ; ;

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{ 15.73**2-13.8**2-28.05**2 }{ 2 * 13.8 * 28.05 } ) = 19° 28'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13.8**2-15.73**2-28.05**2 }{ 2 * 15.73 * 28.05 } ) = 17° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28.05**2-15.73**2-13.8**2 }{ 2 * 13.8 * 15.73 } ) = 143° 31'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.51 }{ 28.79 } = 2.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15.73 }{ 2 * sin 19° 28'1" } = 23.6 ; ;





#2 Obtuse scalene triangle.

Sides: a = 15.73   b = 13.8   c = 2.03215579716

Area: T = 4.67215745802
Perimeter: p = 31.56215579716
Semiperimeter: s = 15.78107789858

Angle ∠ A = α = 160.5333152575° = 160°31'59″ = 2.8021832071 rad
Angle ∠ B = β = 17° = 0.29767059728 rad
Angle ∠ C = γ = 2.46768474254° = 2°28'1″ = 0.04330546097 rad

Height: ha = 0.59439700674
Height: hb = 0.67770397942
Height: hc = 4.59990069153

Median: ma = 5.95219231259
Median: mb = 8.84113835963
Median: mc = 14.76215935133

Inradius: r = 0.29660294029
Circumradius: R = 23.66000949768

Vertex coordinates: A[2.03215579716; 0] B[0; 0] C[15.04326738113; 4.59990069153]
Centroid: CG[5.69114105943; 1.53330023051]
Coordinates of the circumscribed circle: U[1.01657789858; 23.57882246144]
Coordinates of the inscribed circle: I[1.98107789858; 0.29660294029]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 19.46768474254° = 19°28'1″ = 2.8021832071 rad
∠ B' = β' = 163° = 0.29767059728 rad
∠ C' = γ' = 177.5333152575° = 177°31'59″ = 0.04330546097 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 15.73 ; ; b = 13.8 ; ; beta = 17° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 13.8**2 = 15.73**2 + c**2 -2 * 13.8 * c * cos (17° ) ; ; ; ; c**2 -30.085c +56.993 =0 ; ; p=1; q=-30.0853476226; r=56.9929 ; ; D = q**2 - 4pr = 30.085**2 - 4 * 1 * 56.993 = 677.156541573 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 30.09 ± sqrt{ 677.16 } }{ 2 } ; ; c_{1,2} = 15.0426738113 ± 13.0111158397 ; ;
c_{1} = 28.053789651 ; ; c_{2} = 2.03155797164 ; ; ; ; (c -28.053789651) (c -2.03155797164) = 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 = 15.73 ; ; b = 13.8 ; ; c = 2.03 ; ;

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

p = a+b+c = 15.73+13.8+2.03 = 31.56 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.56 }{ 2 } = 15.78 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.78 * (15.78-15.73)(15.78-13.8)(15.78-2.03) } ; ; T = sqrt{ 21.82 } = 4.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.67 }{ 15.73 } = 0.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.67 }{ 13.8 } = 0.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.67 }{ 2.03 } = 4.6 ; ;

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{ 15.73**2-13.8**2-2.03**2 }{ 2 * 13.8 * 2.03 } ) = 160° 31'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13.8**2-15.73**2-2.03**2 }{ 2 * 15.73 * 2.03 } ) = 17° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.03**2-15.73**2-13.8**2 }{ 2 * 13.8 * 15.73 } ) = 2° 28'1" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.67 }{ 15.78 } = 0.3 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15.73 }{ 2 * sin 160° 31'59" } = 23.6 ; ;




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