Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 33   b = 45   c = 18.26598906788

Area: T = 260.9233231769
Perimeter: p = 96.26598906788
Semiperimeter: s = 48.13299453394

Angle ∠ A = α = 39.42663110069° = 39°25'35″ = 0.6888118939 rad
Angle ∠ B = β = 120° = 2.09443951024 rad
Angle ∠ C = γ = 20.57436889931° = 20°34'25″ = 0.35990786122 rad

Height: ha = 15.81435291981
Height: hb = 11.59765880786
Height: hc = 28.57988383249

Median: ma = 30.11658065441
Median: mb = 14.3166487132
Median: mc = 38.38880723415

Inradius: r = 5.42112243527
Circumradius: R = 25.98107621135

Vertex coordinates: A[18.26598906788; 0] B[0; 0] C[-16.5; 28.57988383249]
Centroid: CG[0.58766302263; 9.52662794416]
Coordinates of the circumscribed circle: U[9.13299453394; 24.32437352826]
Coordinates of the inscribed circle: I[3.13299453394; 5.42112243527]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.5743688993° = 140°34'25″ = 0.6888118939 rad
∠ B' = β' = 60° = 2.09443951024 rad
∠ C' = γ' = 159.4266311007° = 159°25'35″ = 0.35990786122 rad

Calculate another triangle




How did we calculate this triangle?

1. Use Law of Cosines

a = 33 ; ; b = 45 ; ; beta = 120° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 45**2 = 33**2 + c**2 -2 * 45 * c * cos (120° ) ; ; ; ; c**2 +33c -936 =0 ; ; p=1; q=33; r=-936 ; ; D = q**2 - 4pr = 33**2 - 4 * 1 * (-936) = 4833 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ -33 ± sqrt{ 4833 } }{ 2 } ; ; c_{1,2} = -16.5 ± 34.7598906788 ; ; c_{1} = 18.2598906788 ; ; c_{2} = -51.2598906788 ; ;
 ; ; (c -18.2598906788) (c +51.2598906788) = 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 = 33 ; ; b = 45 ; ; c = 18.26 ; ;

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

p = a+b+c = 33+45+18.26 = 96.26 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 96.26 }{ 2 } = 48.13 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 48.13 * (48.13-33)(48.13-45)(48.13-18.26) } ; ; T = sqrt{ 68080.93 } = 260.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 260.92 }{ 33 } = 15.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 260.92 }{ 45 } = 11.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 260.92 }{ 18.26 } = 28.58 ; ;

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{ 33**2-45**2-18.26**2 }{ 2 * 45 * 18.26 } ) = 39° 25'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 45**2-33**2-18.26**2 }{ 2 * 33 * 18.26 } ) = 120° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18.26**2-33**2-45**2 }{ 2 * 45 * 33 } ) = 20° 34'25" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 260.92 }{ 48.13 } = 5.42 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 33 }{ 2 * sin 39° 25'35" } = 25.98 ; ;




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

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