Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=10.26109558648 and with side c=2.15325187605

#1 Obtuse scalene triangle.

Sides: a = 6.37   b = 4.3   c = 10.26109558648

Area: T = 7.35216578966
Perimeter: p = 20.93109558648
Semiperimeter: s = 10.46554779324

Angle ∠ A = α = 19.46656365902° = 19°27'56″ = 0.34397394495 rad
Angle ∠ B = β = 13° = 0.22768928028 rad
Angle ∠ C = γ = 147.534436341° = 147°32'4″ = 2.57549604013 rad

Height: ha = 2.30882128404
Height: hb = 3.41993757659
Height: hc = 1.43329382162

Median: ma = 7.19333568402
Median: mb = 8.26549596266
Median: mc = 1.79221066333

Inradius: r = 0.70224674787
Circumradius: R = 9.55876346876

Vertex coordinates: A[10.26109558648; 0] B[0; 0] C[6.20767373127; 1.43329382162]
Centroid: CG[5.48992310592; 0.47876460721]
Coordinates of the circumscribed circle: U[5.13304779324; -8.06439058158]
Coordinates of the inscribed circle: I[6.16554779324; 0.70224674787]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.534436341° = 160°32'4″ = 0.34397394495 rad
∠ B' = β' = 167° = 0.22768928028 rad
∠ C' = γ' = 32.46656365902° = 32°27'56″ = 2.57549604013 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 = 6.37 ; ; b = 4.3 ; ; c = 10.26 ; ;

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

p = a+b+c = 6.37+4.3+10.26 = 20.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.93 }{ 2 } = 10.47 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.47 * (10.47-6.37)(10.47-4.3)(10.47-10.26) } ; ; T = sqrt{ 54.05 } = 7.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.35 }{ 6.37 } = 2.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.35 }{ 4.3 } = 3.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.35 }{ 10.26 } = 1.43 ; ;

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{ 6.37**2-4.3**2-10.26**2 }{ 2 * 4.3 * 10.26 } ) = 19° 27'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.3**2-6.37**2-10.26**2 }{ 2 * 6.37 * 10.26 } ) = 13° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.26**2-6.37**2-4.3**2 }{ 2 * 4.3 * 6.37 } ) = 147° 32'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.35 }{ 10.47 } = 0.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.37 }{ 2 * sin 19° 27'56" } = 9.56 ; ;





#2 Obtuse scalene triangle.

Sides: a = 6.37   b = 4.3   c = 2.15325187605

Area: T = 1.54222131965
Perimeter: p = 12.82325187605
Semiperimeter: s = 6.41112593803

Angle ∠ A = α = 160.534436341° = 160°32'4″ = 2.80218532041 rad
Angle ∠ B = β = 13° = 0.22768928028 rad
Angle ∠ C = γ = 6.46656365902° = 6°27'56″ = 0.11328466467 rad

Height: ha = 0.48442113647
Height: hb = 0.71773084635
Height: hc = 1.43329382162

Median: ma = 1.1910564365
Median: mb = 4.24105917638
Median: mc = 5.32768298026

Inradius: r = 0.24105476218
Circumradius: R = 9.55876346876

Vertex coordinates: A[2.15325187605; 0] B[0; 0] C[6.20767373127; 1.43329382162]
Centroid: CG[2.78664186911; 0.47876460721]
Coordinates of the circumscribed circle: U[1.07662593803; 9.4976844032]
Coordinates of the inscribed circle: I[2.11112593803; 0.24105476218]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 19.46656365902° = 19°27'56″ = 2.80218532041 rad
∠ B' = β' = 167° = 0.22768928028 rad
∠ C' = γ' = 173.534436341° = 173°32'4″ = 0.11328466467 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 6.37 ; ; b = 4.3 ; ; beta = 13° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 4.3**2 = 6.37**2 + c**2 -2 * 4.3 * c * cos (13° ) ; ; ; ; c**2 -12.413c +22.087 =0 ; ; p=1; q=-12.4134746254; r=22.0869 ; ; D = q**2 - 4pr = 12.413**2 - 4 * 1 * 22.087 = 65.7467522746 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 12.41 ± sqrt{ 65.75 } }{ 2 } ; ; c_{1,2} = 6.20673731268 ± 4.05421855216 ; ;
c_{1} = 10.2609558648 ; ; c_{2} = 2.15251876053 ; ; ; ; (c -10.2609558648) (c -2.15251876053) = 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 = 6.37 ; ; b = 4.3 ; ; c = 2.15 ; ;

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

p = a+b+c = 6.37+4.3+2.15 = 12.82 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.82 }{ 2 } = 6.41 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.41 * (6.41-6.37)(6.41-4.3)(6.41-2.15) } ; ; T = sqrt{ 2.38 } = 1.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.54 }{ 6.37 } = 0.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.54 }{ 4.3 } = 0.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.54 }{ 2.15 } = 1.43 ; ;

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{ 6.37**2-4.3**2-2.15**2 }{ 2 * 4.3 * 2.15 } ) = 160° 32'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.3**2-6.37**2-2.15**2 }{ 2 * 6.37 * 2.15 } ) = 13° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.15**2-6.37**2-4.3**2 }{ 2 * 4.3 * 6.37 } ) = 6° 27'56" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.54 }{ 6.41 } = 0.24 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.37 }{ 2 * sin 160° 32'4" } = 9.56 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.