Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=7.51550398384 and with side c=3.83223150135

#1 Acute scalene triangle.

Sides: a = 7.2   b = 4.8   c = 7.51550398384

Area: T = 16.65661938506
Perimeter: p = 19.51550398384
Semiperimeter: s = 9.75875199192

Angle ∠ A = α = 67.44220807656° = 67°26'31″ = 1.17770863638 rad
Angle ∠ B = β = 38° = 0.66332251158 rad
Angle ∠ C = γ = 74.55879192344° = 74°33'29″ = 1.30112811741 rad

Height: ha = 4.6276720514
Height: hb = 6.94400807711
Height: hc = 4.43327626223

Median: ma = 5.17766699611
Median: mb = 6.95768607781
Median: mc = 4.82991866869

Inradius: r = 1.70770110016
Circumradius: R = 3.89882461892

Vertex coordinates: A[7.51550398384; 0] B[0; 0] C[5.6743677426; 4.43327626223]
Centroid: CG[4.39662390881; 1.47875875408]
Coordinates of the circumscribed circle: U[3.75875199192; 1.03879631054]
Coordinates of the inscribed circle: I[4.95875199192; 1.70770110016]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.5587919234° = 112°33'29″ = 1.17770863638 rad
∠ B' = β' = 142° = 0.66332251158 rad
∠ C' = γ' = 105.4422080766° = 105°26'31″ = 1.30112811741 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 = 7.2 ; ; b = 4.8 ; ; c = 7.52 ; ;

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

p = a+b+c = 7.2+4.8+7.52 = 19.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19.52 }{ 2 } = 9.76 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.76 * (9.76-7.2)(9.76-4.8)(9.76-7.52) } ; ; T = sqrt{ 277.43 } = 16.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.66 }{ 7.2 } = 4.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.66 }{ 4.8 } = 6.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.66 }{ 7.52 } = 4.43 ; ;

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{ 7.2**2-4.8**2-7.52**2 }{ 2 * 4.8 * 7.52 } ) = 67° 26'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.8**2-7.2**2-7.52**2 }{ 2 * 7.2 * 7.52 } ) = 38° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.52**2-7.2**2-4.8**2 }{ 2 * 4.8 * 7.2 } ) = 74° 33'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.66 }{ 9.76 } = 1.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.2 }{ 2 * sin 67° 26'31" } = 3.9 ; ;





#2 Obtuse scalene triangle.

Sides: a = 7.2   b = 4.8   c = 3.83223150135

Area: T = 8.49438713745
Perimeter: p = 15.83223150135
Semiperimeter: s = 7.91661575068

Angle ∠ A = α = 112.5587919234° = 112°33'29″ = 1.96545062898 rad
Angle ∠ B = β = 38° = 0.66332251158 rad
Angle ∠ C = γ = 29.44220807656° = 29°26'31″ = 0.5143861248 rad

Height: ha = 2.35994087151
Height: hb = 3.53991130727
Height: hc = 4.43327626223

Median: ma = 2.43296747069
Median: mb = 5.24443607028
Median: mc = 5.8111053296

Inradius: r = 1.07329790769
Circumradius: R = 3.89882461892

Vertex coordinates: A[3.83223150135; 0] B[0; 0] C[5.6743677426; 4.43327626223]
Centroid: CG[3.16986641465; 1.47875875408]
Coordinates of the circumscribed circle: U[1.91661575068; 3.3954799517]
Coordinates of the inscribed circle: I[3.11661575068; 1.07329790769]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 67.44220807656° = 67°26'31″ = 1.96545062898 rad
∠ B' = β' = 142° = 0.66332251158 rad
∠ C' = γ' = 150.5587919234° = 150°33'29″ = 0.5143861248 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 7.2 ; ; b = 4.8 ; ; beta = 38° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 4.8**2 = 7.2**2 + c**2 -2 * 4.8 * c * cos (38° ) ; ; ; ; c**2 -11.347c +28.8 =0 ; ; p=1; q=-11.3473548519; r=28.8 ; ; D = q**2 - 4pr = 11.347**2 - 4 * 1 * 28.8 = 13.5624621358 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 11.35 ± sqrt{ 13.56 } }{ 2 } ; ; c_{1,2} = 5.67367742597 ± 1.84136241244 ; ; c_{1} = 7.51503983841 ; ;
c_{2} = 3.83231501353 ; ; ; ; (c -7.51503983841) (c -3.83231501353) = 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 = 7.2 ; ; b = 4.8 ; ; c = 3.83 ; ;

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

p = a+b+c = 7.2+4.8+3.83 = 15.83 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.83 }{ 2 } = 7.92 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.92 * (7.92-7.2)(7.92-4.8)(7.92-3.83) } ; ; T = sqrt{ 72.15 } = 8.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.49 }{ 7.2 } = 2.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.49 }{ 4.8 } = 3.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.49 }{ 3.83 } = 4.43 ; ;

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{ 7.2**2-4.8**2-3.83**2 }{ 2 * 4.8 * 3.83 } ) = 112° 33'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.8**2-7.2**2-3.83**2 }{ 2 * 7.2 * 3.83 } ) = 38° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.83**2-7.2**2-4.8**2 }{ 2 * 4.8 * 7.2 } ) = 29° 26'31" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.49 }{ 7.92 } = 1.07 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.2 }{ 2 * sin 112° 33'29" } = 3.9 ; ;




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

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