Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=5.73222225734 and with side c=1.32440937355

#1 Acute scalene triangle.

Sides: a = 12.8   b = 12.5   c = 5.73222225734

Area: T = 35.26550623514
Perimeter: p = 31.03222225734
Semiperimeter: s = 15.51661112867

Angle ∠ A = α = 79.84442169226° = 79°50'39″ = 1.3943544474 rad
Angle ∠ B = β = 74° = 1.29215436465 rad
Angle ∠ C = γ = 26.15657830774° = 26°9'21″ = 0.45765045331 rad

Height: ha = 5.51101659924
Height: hb = 5.64224099762
Height: hc = 12.3044149708

Median: ma = 7.32108051344
Median: mb = 7.76997849201
Median: mc = 12.32219481452

Inradius: r = 2.27328028757
Circumradius: R = 6.50218714741

Vertex coordinates: A[5.73222225734; 0] B[0; 0] C[3.52881581545; 12.3044149708]
Centroid: CG[3.0876793576; 4.1011383236]
Coordinates of the circumscribed circle: U[2.86661112867; 5.8366072203]
Coordinates of the inscribed circle: I[3.01661112867; 2.27328028757]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.1565783077° = 100°9'21″ = 1.3943544474 rad
∠ B' = β' = 106° = 1.29215436465 rad
∠ C' = γ' = 153.8444216923° = 153°50'39″ = 0.45765045331 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 12.8 ; ; b = 12.5 ; ; beta = 74° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 12.5**2 = 12.8**2 + c**2 -2 * 12.8 * c * cos (74° ) ; ; ; ; c**2 -7.056c +7.59 =0 ; ; p=1; q=-7.056; r=7.59 ; ; D = q**2 - 4pr = 7.056**2 - 4 * 1 * 7.59 = 19.4315998515 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 7.06 ± sqrt{ 19.43 } }{ 2 } ; ; c_{1,2} = 3.52815815 ± 2.20406441895 ; ; c_{1} = 5.73222256895 ; ;
c_{2} = 1.32409373105 ; ; ; ; text{ Factored form: } ; ; (c -5.73222256895) (c -1.32409373105) = 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 = 12.8 ; ; b = 12.5 ; ; c = 5.73 ; ;

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

p = a+b+c = 12.8+12.5+5.73 = 31.03 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.03 }{ 2 } = 15.52 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.52 * (15.52-12.8)(15.52-12.5)(15.52-5.73) } ; ; T = sqrt{ 1243.62 } = 35.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.27 }{ 12.8 } = 5.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.27 }{ 12.5 } = 5.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.27 }{ 5.73 } = 12.3 ; ;

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{ 12.5**2+5.73**2-12.8**2 }{ 2 * 12.5 * 5.73 } ) = 79° 50'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.8**2+5.73**2-12.5**2 }{ 2 * 12.8 * 5.73 } ) = 74° ; ; gamma = 180° - alpha - beta = 180° - 79° 50'39" - 74° = 26° 9'21" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.27 }{ 15.52 } = 2.27 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.8 }{ 2 * sin 79° 50'39" } = 6.5 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 5.73**2 - 12.8**2 } }{ 2 } = 7.321 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.73**2+2 * 12.8**2 - 12.5**2 } }{ 2 } = 7.7 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 12.8**2 - 5.73**2 } }{ 2 } = 12.322 ; ;







#2 Obtuse scalene triangle.

Sides: a = 12.8   b = 12.5   c = 1.32440937355

Area: T = 8.14659237746
Perimeter: p = 26.62440937355
Semiperimeter: s = 13.31220468678

Angle ∠ A = α = 100.1565783077° = 100°9'21″ = 1.74880481796 rad
Angle ∠ B = β = 74° = 1.29215436465 rad
Angle ∠ C = γ = 5.84442169226° = 5°50'39″ = 0.10220008275 rad

Height: ha = 1.27328005898
Height: hb = 1.30333478039
Height: hc = 12.3044149708

Median: ma = 6.16877882673
Median: mb = 6.6133177157
Median: mc = 12.63435542879

Inradius: r = 0.61219212061
Circumradius: R = 6.50218714741

Vertex coordinates: A[1.32440937355; 0] B[0; 0] C[3.52881581545; 12.3044149708]
Centroid: CG[1.61774172967; 4.1011383236]
Coordinates of the circumscribed circle: U[0.66220468678; 6.4688077505]
Coordinates of the inscribed circle: I[0.81220468678; 0.61219212061]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 79.84442169226° = 79°50'39″ = 1.74880481796 rad
∠ B' = β' = 106° = 1.29215436465 rad
∠ C' = γ' = 174.1565783077° = 174°9'21″ = 0.10220008275 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 12.8 ; ; b = 12.5 ; ; beta = 74° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 12.5**2 = 12.8**2 + c**2 -2 * 12.8 * c * cos (74° ) ; ; ; ; c**2 -7.056c +7.59 =0 ; ; p=1; q=-7.056; r=7.59 ; ; D = q**2 - 4pr = 7.056**2 - 4 * 1 * 7.59 = 19.4315998515 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 7.06 ± sqrt{ 19.43 } }{ 2 } ; ; c_{1,2} = 3.52815815 ± 2.20406441895 ; ; c_{1} = 5.73222256895 ; ; : Nr. 1
c_{2} = 1.32409373105 ; ; ; ; text{ Factored form: } ; ; (c -5.73222256895) (c -1.32409373105) = 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 = 12.8 ; ; b = 12.5 ; ; c = 1.32 ; ;

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

p = a+b+c = 12.8+12.5+1.32 = 26.62 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.62 }{ 2 } = 13.31 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.31 * (13.31-12.8)(13.31-12.5)(13.31-1.32) } ; ; T = sqrt{ 66.36 } = 8.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.15 }{ 12.8 } = 1.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.15 }{ 12.5 } = 1.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.15 }{ 1.32 } = 12.3 ; ;

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{ 12.5**2+1.32**2-12.8**2 }{ 2 * 12.5 * 1.32 } ) = 100° 9'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.8**2+1.32**2-12.5**2 }{ 2 * 12.8 * 1.32 } ) = 74° ; ; gamma = 180° - alpha - beta = 180° - 100° 9'21" - 74° = 5° 50'39" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.15 }{ 13.31 } = 0.61 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.8 }{ 2 * sin 100° 9'21" } = 6.5 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 1.32**2 - 12.8**2 } }{ 2 } = 6.168 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.32**2+2 * 12.8**2 - 12.5**2 } }{ 2 } = 6.613 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 12.8**2 - 1.32**2 } }{ 2 } = 12.634 ; ;
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.