Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=93.37992172023 and with side c=20.93661360972

#1 Obtuse scalene triangle.

Sides: a = 66   b = 49   c = 93.37992172023

Area: T = 1540.757708384
Perimeter: p = 208.3799217202
Semiperimeter: s = 104.1989608601

Angle ∠ A = α = 42.33554018762° = 42°20'7″ = 0.73988921529 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 107.6654598124° = 107°39'53″ = 1.87991017251 rad

Height: ha = 46.69896086012
Height: hb = 62.88880442383
Height: hc = 33

Median: ma = 66.86880723713
Median: mb = 77.05657532093
Median: mc = 34.62105206297

Inradius: r = 14.78880110553
Circumradius: R = 49

Vertex coordinates: A[93.37992172023; 0] B[0; 0] C[57.15876766498; 33]
Centroid: CG[50.17989646174; 11]
Coordinates of the circumscribed circle: U[46.69896086012; -14.86987742827]
Coordinates of the inscribed circle: I[55.19896086012; 14.78880110553]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.6654598124° = 137°39'53″ = 0.73988921529 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 72.33554018762° = 72°20'7″ = 1.87991017251 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 = 66 ; ; b = 49 ; ; c = 93.38 ; ;

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

p = a+b+c = 66+49+93.38 = 208.38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 208.38 }{ 2 } = 104.19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 104.19 * (104.19-66)(104.19-49)(104.19-93.38) } ; ; T = sqrt{ 2373932.39 } = 1540.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1540.76 }{ 66 } = 46.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1540.76 }{ 49 } = 62.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1540.76 }{ 93.38 } = 33 ; ;

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{ 66**2-49**2-93.38**2 }{ 2 * 49 * 93.38 } ) = 42° 20'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 49**2-66**2-93.38**2 }{ 2 * 66 * 93.38 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 93.38**2-66**2-49**2 }{ 2 * 49 * 66 } ) = 107° 39'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1540.76 }{ 104.19 } = 14.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 66 }{ 2 * sin 42° 20'7" } = 49 ; ;





#2 Obtuse scalene triangle.

Sides: a = 66   b = 49   c = 20.93661360972

Area: T = 345.4466245604
Perimeter: p = 135.9366136097
Semiperimeter: s = 67.96880680486

Angle ∠ A = α = 137.6654598124° = 137°39'53″ = 2.40327005007 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 12.33554018762° = 12°20'7″ = 0.21552933773 rad

Height: ha = 10.46880680486
Height: hb = 14.10998467594
Height: hc = 33

Median: ma = 18.18440836266
Median: mb = 42.39899858143
Median: mc = 57.17444659033

Inradius: r = 5.08224785156
Circumradius: R = 49

Vertex coordinates: A[20.93661360972; 0] B[0; 0] C[57.15876766498; 33]
Centroid: CG[26.03112709157; 11]
Coordinates of the circumscribed circle: U[10.46880680486; 47.86987742827]
Coordinates of the inscribed circle: I[18.96880680486; 5.08224785156]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.33554018762° = 42°20'7″ = 2.40327005007 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 167.6654598124° = 167°39'53″ = 0.21552933773 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 66 ; ; b = 49 ; ; beta = 30° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 49**2 = 66**2 + c**2 -2 * 49 * c * cos (30° ) ; ; ; ; c**2 -114.315c +1955 =0 ; ; p=1; q=-114.3153533; r=1955 ; ; D = q**2 - 4pr = 114.315**2 - 4 * 1 * 1955 = 5248 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 114.32 ± sqrt{ 5248 } }{ 2 } = fraction{ 114.32 ± 8 sqrt{ 82 } }{ 2 } ; ; c_{1,2} = 57.1576766498 ± 36.2215405525 ; ;
c_{1} = 93.3792172023 ; ; c_{2} = 20.9361360972 ; ; ; ; (c -93.3792172023) (c -20.9361360972) = 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 = 66 ; ; b = 49 ; ; c = 20.94 ; ;

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

p = a+b+c = 66+49+20.94 = 135.94 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 135.94 }{ 2 } = 67.97 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 67.97 * (67.97-66)(67.97-49)(67.97-20.94) } ; ; T = sqrt{ 119333.11 } = 345.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 345.45 }{ 66 } = 10.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 345.45 }{ 49 } = 14.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 345.45 }{ 20.94 } = 33 ; ;

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{ 66**2-49**2-20.94**2 }{ 2 * 49 * 20.94 } ) = 137° 39'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 49**2-66**2-20.94**2 }{ 2 * 66 * 20.94 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20.94**2-66**2-49**2 }{ 2 * 49 * 66 } ) = 12° 20'7" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 345.45 }{ 67.97 } = 5.08 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 66 }{ 2 * sin 137° 39'53" } = 49 ; ;




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

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