Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=139.9321811185 and with side c=66.18222349154

#1 Obtuse scalene triangle.

Sides: a = 119   b = 70   c = 139.9321811185

Area: T = 4162.971138276
Perimeter: p = 328.9321811185
Semiperimeter: s = 164.4665905593

Angle ∠ A = α = 58.21216693829° = 58°12'42″ = 1.01659852938 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 91.78883306171° = 91°47'18″ = 1.60220085842 rad

Height: ha = 69.96659055927
Height: hb = 118.9422039507
Height: hc = 59.5

Median: ma = 93.27548942149
Median: mb = 125.0843795477
Median: mc = 68.08328323045

Inradius: r = 25.31220631158
Circumradius: R = 70

Vertex coordinates: A[139.9321811185; 0] B[0; 0] C[103.057702305; 59.5]
Centroid: CG[80.99662780786; 19.83333333333]
Coordinates of the circumscribed circle: U[69.96659055927; -2.18545032841]
Coordinates of the inscribed circle: I[94.46659055927; 25.31220631158]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.7888330617° = 121°47'18″ = 1.01659852938 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 88.21216693829° = 88°12'42″ = 1.60220085842 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 119 ; ; b = 70 ; ; beta = 30° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 70**2 = 119**2 + c**2 -2 * 119 * c * cos (30° ) ; ; ; ; c**2 -206.114c +9261 =0 ; ; p=1; q=-206.114; r=9261 ; ; D = q**2 - 4pr = 206.114**2 - 4 * 1 * 9261 = 5439 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 206.11 ± sqrt{ 5439 } }{ 2 } ; ; c_{1,2} = 103.05702305 ± 36.874788135 ; ; c_{1} = 139.931811185 ; ;
c_{2} = 66.182234915 ; ; ; ; text{ Factored form: } ; ; (c -139.931811185) (c -66.182234915) = 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 = 119 ; ; b = 70 ; ; c = 139.93 ; ;

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

p = a+b+c = 119+70+139.93 = 328.93 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 328.93 }{ 2 } = 164.47 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 164.47 * (164.47-119)(164.47-70)(164.47-139.93) } ; ; T = sqrt{ 17330330.73 } = 4162.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4162.97 }{ 119 } = 69.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4162.97 }{ 70 } = 118.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4162.97 }{ 139.93 } = 59.5 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 70**2+139.93**2-119**2 }{ 2 * 70 * 139.93 } ) = 58° 12'42" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 119**2+139.93**2-70**2 }{ 2 * 119 * 139.93 } ) = 30° ; ; gamma = 180° - alpha - beta = 180° - 58° 12'42" - 30° = 91° 47'18" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4162.97 }{ 164.47 } = 25.31 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 119 }{ 2 * sin 58° 12'42" } = 70 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 139.93**2 - 119**2 } }{ 2 } = 93.275 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 139.93**2+2 * 119**2 - 70**2 } }{ 2 } = 125.084 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 119**2 - 139.93**2 } }{ 2 } = 68.083 ; ;







#2 Obtuse scalene triangle.

Sides: a = 119   b = 70   c = 66.18222349154

Area: T = 1968.921148873
Perimeter: p = 255.1822234915
Semiperimeter: s = 127.5911117458

Angle ∠ A = α = 121.7888330617° = 121°47'18″ = 2.12656073598 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 28.21216693829° = 28°12'42″ = 0.49223865182 rad

Height: ha = 33.09111174577
Height: hb = 56.25548996781
Height: hc = 59.5

Median: ma = 33.16331438376
Median: mb = 89.69769570788
Median: mc = 91.84548580237

Inradius: r = 15.4311493414
Circumradius: R = 70

Vertex coordinates: A[66.18222349154; 0] B[0; 0] C[103.057702305; 59.5]
Centroid: CG[56.41330859886; 19.83333333333]
Coordinates of the circumscribed circle: U[33.09111174577; 61.68545032841]
Coordinates of the inscribed circle: I[57.59111174577; 15.4311493414]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 58.21216693829° = 58°12'42″ = 2.12656073598 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 151.7888330617° = 151°47'18″ = 0.49223865182 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 119 ; ; b = 70 ; ; beta = 30° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 70**2 = 119**2 + c**2 -2 * 119 * c * cos (30° ) ; ; ; ; c**2 -206.114c +9261 =0 ; ; p=1; q=-206.114; r=9261 ; ; D = q**2 - 4pr = 206.114**2 - 4 * 1 * 9261 = 5439 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 206.11 ± sqrt{ 5439 } }{ 2 } ; ; c_{1,2} = 103.05702305 ± 36.874788135 ; ; c_{1} = 139.931811185 ; ; : Nr. 1
c_{2} = 66.182234915 ; ; ; ; text{ Factored form: } ; ; (c -139.931811185) (c -66.182234915) = 0 ; ; ; ; c>0 ; ; : Nr. 1


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 = 119 ; ; b = 70 ; ; c = 66.18 ; ;

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

p = a+b+c = 119+70+66.18 = 255.18 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 255.18 }{ 2 } = 127.59 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 127.59 * (127.59-119)(127.59-70)(127.59-66.18) } ; ; T = sqrt{ 3876651.83 } = 1968.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1968.92 }{ 119 } = 33.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1968.92 }{ 70 } = 56.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1968.92 }{ 66.18 } = 59.5 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 70**2+66.18**2-119**2 }{ 2 * 70 * 66.18 } ) = 121° 47'18" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 119**2+66.18**2-70**2 }{ 2 * 119 * 66.18 } ) = 30° ; ; gamma = 180° - alpha - beta = 180° - 121° 47'18" - 30° = 28° 12'42" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1968.92 }{ 127.59 } = 15.43 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 119 }{ 2 * sin 121° 47'18" } = 70 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 66.18**2 - 119**2 } }{ 2 } = 33.163 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 66.18**2+2 * 119**2 - 70**2 } }{ 2 } = 89.697 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 119**2 - 66.18**2 } }{ 2 } = 91.845 ; ;
Calculate another triangle

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

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