Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 4.5   b = 12.8   c = 14.60325126149

Area: T = 27.86331742998
Perimeter: p = 31.90325126149
Semiperimeter: s = 15.95112563074

Angle ∠ A = α = 17.34660359884° = 17°20'46″ = 0.30327454402 rad
Angle ∠ B = β = 58° = 1.01222909662 rad
Angle ∠ C = γ = 104.6543964012° = 104°39'14″ = 1.82765562473 rad

Height: ha = 12.38436330221
Height: hb = 4.35436209843
Height: hc = 3.81662164327

Median: ma = 13.54552643877
Median: mb = 8.70552677922
Median: mc = 6.22438779176

Inradius: r = 1.74767698947
Circumradius: R = 7.54767417815

Vertex coordinates: A[14.60325126149; 0] B[0; 0] C[2.3854636689; 3.81662164327]
Centroid: CG[5.66223831013; 1.27220721442]
Coordinates of the circumscribed circle: U[7.30112563074; -1.90991798894]
Coordinates of the inscribed circle: I[3.15112563074; 1.74767698947]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.6543964012° = 162°39'14″ = 0.30327454402 rad
∠ B' = β' = 122° = 1.01222909662 rad
∠ C' = γ' = 75.34660359884° = 75°20'46″ = 1.82765562473 rad

Calculate another triangle




How did we calculate this triangle?

1. Use Law of Cosines

a = 4.5 ; ; b = 12.8 ; ; beta = 58° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 12.8**2 = 4.5**2 + c**2 -2 * 12.8 * c * cos (58° ) ; ; ; ; c**2 -4.769c -143.59 =0 ; ; p=1; q=-4.7692733781; r=-143.59 ; ; D = q**2 - 4pr = 4.769**2 - 4 * 1 * (-143.59) = 597.105968555 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 4.77 ± sqrt{ 597.11 } }{ 2 } ; ; c_{1,2} = 2.38463668905 ± 12.2178759258 ; ;
c_{1} = 14.6025126149 ; ; c_{2} = -9.83323923677 ; ; ; ; (c -14.6025126149) (c +9.83323923677) = 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 = 4.5 ; ; b = 12.8 ; ; c = 14.6 ; ;

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

p = a+b+c = 4.5+12.8+14.6 = 31.9 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.9 }{ 2 } = 15.95 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.95 * (15.95-4.5)(15.95-12.8)(15.95-14.6) } ; ; T = sqrt{ 776.36 } = 27.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.86 }{ 4.5 } = 12.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.86 }{ 12.8 } = 4.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.86 }{ 14.6 } = 3.82 ; ;

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{ 4.5**2-12.8**2-14.6**2 }{ 2 * 12.8 * 14.6 } ) = 17° 20'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12.8**2-4.5**2-14.6**2 }{ 2 * 4.5 * 14.6 } ) = 58° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14.6**2-4.5**2-12.8**2 }{ 2 * 12.8 * 4.5 } ) = 104° 39'14" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.86 }{ 15.95 } = 1.75 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.5 }{ 2 * sin 17° 20'46" } = 7.55 ; ;




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

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