Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=69.10109804877 and with side c=3.95107398893

#1 Obtuse scalene triangle.

Sides: a = 47   b = 44   c = 69.10109804877

Area: T = 1021.936641747
Perimeter: p = 160.1010980488
Semiperimeter: s = 80.05504902438

Angle ∠ A = α = 42.23993030744° = 42°14'21″ = 0.73772149124 rad
Angle ∠ B = β = 39° = 0.68106784083 rad
Angle ∠ C = γ = 98.76106969256° = 98°45'39″ = 1.72436993329 rad

Height: ha = 43.48766560624
Height: hb = 46.45216553394
Height: hc = 29.57880583793

Median: ma = 52.94554696096
Median: mb = 54.84549883962
Median: mc = 29.64439475089

Inradius: r = 12.76661481442
Circumradius: R = 34.95883460394

Vertex coordinates: A[69.10109804877; 0] B[0; 0] C[36.52658601885; 29.57880583793]
Centroid: CG[35.20989468921; 9.85993527931]
Coordinates of the circumscribed circle: U[34.55504902438; -5.3244432526]
Coordinates of the inscribed circle: I[36.05504902438; 12.76661481442]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.7610696926° = 137°45'39″ = 0.73772149124 rad
∠ B' = β' = 141° = 0.68106784083 rad
∠ C' = γ' = 81.23993030744° = 81°14'21″ = 1.72436993329 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 = 47 ; ; b = 44 ; ; c = 69.1 ; ;

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

p = a+b+c = 47+44+69.1 = 160.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 160.1 }{ 2 } = 80.05 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 80.05 * (80.05-47)(80.05-44)(80.05-69.1) } ; ; T = sqrt{ 1044354.04 } = 1021.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1021.94 }{ 47 } = 43.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1021.94 }{ 44 } = 46.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1021.94 }{ 69.1 } = 29.58 ; ;

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{ 47**2-44**2-69.1**2 }{ 2 * 44 * 69.1 } ) = 42° 14'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 44**2-47**2-69.1**2 }{ 2 * 47 * 69.1 } ) = 39° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 69.1**2-47**2-44**2 }{ 2 * 44 * 47 } ) = 98° 45'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1021.94 }{ 80.05 } = 12.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 47 }{ 2 * sin 42° 14'21" } = 34.96 ; ;





#2 Obtuse scalene triangle.

Sides: a = 47   b = 44   c = 3.95107398893

Area: T = 58.42876075431
Perimeter: p = 94.95107398893
Semiperimeter: s = 47.47553699446

Angle ∠ A = α = 137.7610696926° = 137°45'39″ = 2.40443777412 rad
Angle ∠ B = β = 39° = 0.68106784083 rad
Angle ∠ C = γ = 3.23993030744° = 3°14'21″ = 0.05765365041 rad

Height: ha = 2.4866281172
Height: hb = 2.65658003429
Height: hc = 29.57880583793

Median: ma = 20.58804317942
Median: mb = 25.06659963464
Median: mc = 45.48218415808

Inradius: r = 1.23106930438
Circumradius: R = 34.95883460394

Vertex coordinates: A[3.95107398893; 0] B[0; 0] C[36.52658601885; 29.57880583793]
Centroid: CG[13.49222000259; 9.85993527931]
Coordinates of the circumscribed circle: U[1.97553699446; 34.90224909053]
Coordinates of the inscribed circle: I[3.47553699446; 1.23106930438]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.23993030744° = 42°14'21″ = 2.40443777412 rad
∠ B' = β' = 141° = 0.68106784083 rad
∠ C' = γ' = 176.7610696926° = 176°45'39″ = 0.05765365041 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 47 ; ; b = 44 ; ; beta = 39° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 44**2 = 47**2 + c**2 -2 * 44 * c * cos (39° ) ; ; ; ; c**2 -73.052c +273 =0 ; ; p=1; q=-73.051720377; r=273 ; ; D = q**2 - 4pr = 73.052**2 - 4 * 1 * 273 = 4244.55385003 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 73.05 ± sqrt{ 4244.55 } }{ 2 } ; ; c_{1,2} = 36.5258601885 ± 32.5751202992 ; ; c_{1} = 69.1009804877 ; ;
c_{2} = 3.95073988926 ; ; ; ; (c -69.1009804877) (c -3.95073988926) = 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 = 47 ; ; b = 44 ; ; c = 3.95 ; ;

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

p = a+b+c = 47+44+3.95 = 94.95 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 94.95 }{ 2 } = 47.48 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 47.48 * (47.48-47)(47.48-44)(47.48-3.95) } ; ; T = sqrt{ 3413.79 } = 58.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.43 }{ 47 } = 2.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.43 }{ 44 } = 2.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.43 }{ 3.95 } = 29.58 ; ;

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{ 47**2-44**2-3.95**2 }{ 2 * 44 * 3.95 } ) = 137° 45'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 44**2-47**2-3.95**2 }{ 2 * 47 * 3.95 } ) = 39° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.95**2-47**2-44**2 }{ 2 * 44 * 47 } ) = 3° 14'21" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.43 }{ 47.48 } = 1.23 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 47 }{ 2 * sin 137° 45'39" } = 34.96 ; ;




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

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