Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=9.30987374751 and with side c=1.95549804739

#1 Obtuse scalene triangle.

Sides: a = 5.78   b = 3.9   c = 9.30987374751

Area: T = 6.05216897948
Perimeter: p = 18.98987374751
Semiperimeter: s = 9.49443687375

Angle ∠ A = α = 19.47546035165° = 19°28'29″ = 0.34398959519 rad
Angle ∠ B = β = 13° = 0.22768928028 rad
Angle ∠ C = γ = 147.5255396483° = 147°31'31″ = 2.57548038989 rad

Height: ha = 2.09440103096
Height: hb = 3.1033430664
Height: hc = 1.33002170941

Median: ma = 6.5255273687
Median: mb = 7.49985329692
Median: mc = 1.62766688831

Inradius: r = 0.63773978052
Circumradius: R = 8.6698552391

Vertex coordinates: A[9.30987374751; 0] B[0; 0] C[5.63218589745; 1.33002170941]
Centroid: CG[4.98801988165; 0.4333405698]
Coordinates of the circumscribed circle: U[4.65443687375; -7.3133046712]
Coordinates of the inscribed circle: I[5.59443687375; 0.63773978052]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.5255396483° = 160°31'31″ = 0.34398959519 rad
∠ B' = β' = 167° = 0.22768928028 rad
∠ C' = γ' = 32.47546035165° = 32°28'29″ = 2.57548038989 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 5.78 ; ; b = 3.9 ; ; beta = 13° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 3.9**2 = 5.78**2 + c**2 -2 * 5.78 * c * cos (13° ) ; ; ; ; c**2 -11.264c +18.198 =0 ; ; p=1; q=-11.264; r=18.198 ; ; D = q**2 - 4pr = 11.264**2 - 4 * 1 * 18.198 = 54.0777420328 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 11.26 ± sqrt{ 54.08 } }{ 2 } ; ; c_{1,2} = 5.63185897 ± 3.6768785006 ; ; c_{1} = 9.3087374706 ; ; c_{2} = 1.9549804694 ; ; ; ; text{ Factored form: } ; ; (c -9.3087374706) (c -1.9549804694) = 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 = 5.78 ; ; b = 3.9 ; ; c = 9.31 ; ;

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

p = a+b+c = 5.78+3.9+9.31 = 18.99 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.99 }{ 2 } = 9.49 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.49 * (9.49-5.78)(9.49-3.9)(9.49-9.31) } ; ; T = sqrt{ 36.62 } = 6.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.05 }{ 5.78 } = 2.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.05 }{ 3.9 } = 3.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.05 }{ 9.31 } = 1.3 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 3.9**2+9.31**2-5.78**2 }{ 2 * 3.9 * 9.31 } ) = 19° 28'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.78**2+9.31**2-3.9**2 }{ 2 * 5.78 * 9.31 } ) = 13° ; ; gamma = 180° - alpha - beta = 180° - 19° 28'29" - 13° = 147° 31'31" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.05 }{ 9.49 } = 0.64 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.78 }{ 2 * sin 19° 28'29" } = 8.67 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 9.31**2 - 5.78**2 } }{ 2 } = 6.525 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.31**2+2 * 5.78**2 - 3.9**2 } }{ 2 } = 7.499 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 5.78**2 - 9.31**2 } }{ 2 } = 1.627 ; ;







#2 Obtuse scalene triangle.

Sides: a = 5.78   b = 3.9   c = 1.95549804739

Area: T = 1.27109495154
Perimeter: p = 11.63549804739
Semiperimeter: s = 5.81774902369

Angle ∠ A = α = 160.5255396483° = 160°31'31″ = 2.80216967017 rad
Angle ∠ B = β = 13° = 0.22768928028 rad
Angle ∠ C = γ = 6.47546035165° = 6°28'29″ = 0.11330031491 rad

Height: ha = 0.44397749188
Height: hb = 0.65217689822
Height: hc = 1.33002170941

Median: ma = 1.07988300731
Median: mb = 3.8498723727
Median: mc = 4.8332567934

Inradius: r = 0.21884704166
Circumradius: R = 8.6698552391

Vertex coordinates: A[1.95549804739; 0] B[0; 0] C[5.63218589745; 1.33002170941]
Centroid: CG[2.52989464828; 0.4333405698]
Coordinates of the circumscribed circle: U[0.97774902369; 8.61332638061]
Coordinates of the inscribed circle: I[1.91774902369; 0.21884704166]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 19.47546035165° = 19°28'29″ = 2.80216967017 rad
∠ B' = β' = 167° = 0.22768928028 rad
∠ C' = γ' = 173.5255396483° = 173°31'31″ = 0.11330031491 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 5.78 ; ; b = 3.9 ; ; beta = 13° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 3.9**2 = 5.78**2 + c**2 -2 * 5.78 * c * cos (13° ) ; ; ; ; c**2 -11.264c +18.198 =0 ; ; p=1; q=-11.264; r=18.198 ; ; D = q**2 - 4pr = 11.264**2 - 4 * 1 * 18.198 = 54.0777420328 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 11.26 ± sqrt{ 54.08 } }{ 2 } ; ; c_{1,2} = 5.63185897 ± 3.6768785006 ; ; c_{1} = 9.3087374706 ; ; c_{2} = 1.9549804694 ; ; ; ; text{ Factored form: } ; ; (c -9.3087374706) (c -1.9549804694) = 0 ; ; ; ; c>0 ; ; : Nr. 1


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 = 5.78 ; ; b = 3.9 ; ; c = 1.95 ; ;

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

p = a+b+c = 5.78+3.9+1.95 = 11.63 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.63 }{ 2 } = 5.82 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.82 * (5.82-5.78)(5.82-3.9)(5.82-1.95) } ; ; T = sqrt{ 1.62 } = 1.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.27 }{ 5.78 } = 0.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.27 }{ 3.9 } = 0.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.27 }{ 1.95 } = 1.3 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 3.9**2+1.95**2-5.78**2 }{ 2 * 3.9 * 1.95 } ) = 160° 31'31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.78**2+1.95**2-3.9**2 }{ 2 * 5.78 * 1.95 } ) = 13° ; ; gamma = 180° - alpha - beta = 180° - 160° 31'31" - 13° = 6° 28'29" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.27 }{ 5.82 } = 0.22 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.78 }{ 2 * sin 160° 31'31" } = 8.67 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 1.95**2 - 5.78**2 } }{ 2 } = 1.079 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.95**2+2 * 5.78**2 - 3.9**2 } }{ 2 } = 3.849 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 5.78**2 - 1.95**2 } }{ 2 } = 4.833 ; ;
Calculate another triangle

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

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