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?

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 ; ;

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

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

2. Semiperimeter of the triangle

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

3. 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 ; ;

4. 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 ; ;

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

6. Inradius

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

7. Circumradius

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





#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 - 2bc cos( beta ) ; ; 70**2 = 119**2 + c**2 -2 * 70 * c * cos (30° ) ; ; ; ; c**2 -206.114c +9261 =0 ; ; p=1; q=-206.114046101; 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} = 66.1822349154 ; ; ; ; (c -139.931811185) (c -66.1822349154) = 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 = 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 119**2-70**2-66.18**2 }{ 2 * 70 * 66.18 } ) = 121° 47'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 70**2-119**2-66.18**2 }{ 2 * 119 * 66.18 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 66.18**2-119**2-70**2 }{ 2 * 70 * 119 } ) = 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 ; ;




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

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