Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=142.5044239816 and with side c=30.70108409409

#1 Obtuse scalene triangle.

Sides: a = 100   b = 75   c = 142.5044239816

Area: T = 3562.60659954
Perimeter: p = 317.5044239816
Semiperimeter: s = 158.7522119908

Angle ∠ A = α = 41.81103148958° = 41°48'37″ = 0.73297276562 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 108.1989685104° = 108°11'23″ = 1.88882662218 rad

Height: ha = 71.2522119908
Height: hb = 95.0032826544
Height: hc = 50

Median: ma = 102.3054590233
Median: mb = 117.2549644702
Median: mc = 52.30333020814

Inradius: r = 22.44113128937
Circumradius: R = 75

Vertex coordinates: A[142.5044239816; 0] B[0; 0] C[86.60325403784; 50]
Centroid: CG[76.36989267315; 16.66766666667]
Coordinates of the circumscribed circle: U[71.2522119908; -23.41222918276]
Coordinates of the inscribed circle: I[83.7522119908; 22.44113128937]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.1989685104° = 138°11'23″ = 0.73297276562 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 71.81103148958° = 71°48'37″ = 1.88882662218 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 = 100 ; ; b = 75 ; ; c = 142.5 ; ;

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

p = a+b+c = 100+75+142.5 = 317.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 317.5 }{ 2 } = 158.75 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 158.75 * (158.75-100)(158.75-75)(158.75-142.5) } ; ; T = sqrt{ 12692161.48 } = 3562.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3562.61 }{ 100 } = 71.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3562.61 }{ 75 } = 95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3562.61 }{ 142.5 } = 50 ; ;

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{ 100**2-75**2-142.5**2 }{ 2 * 75 * 142.5 } ) = 41° 48'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 75**2-100**2-142.5**2 }{ 2 * 100 * 142.5 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 142.5**2-100**2-75**2 }{ 2 * 75 * 100 } ) = 108° 11'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3562.61 }{ 158.75 } = 22.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 41° 48'37" } = 75 ; ;





#2 Obtuse scalene triangle.

Sides: a = 100   b = 75   c = 30.70108409409

Area: T = 767.5211023524
Perimeter: p = 205.7010840941
Semiperimeter: s = 102.855042047

Angle ∠ A = α = 138.1989685104° = 138°11'23″ = 2.41218649974 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 11.81103148958° = 11°48'37″ = 0.20661288806 rad

Height: ha = 15.35504204705
Height: hb = 20.4677227294
Height: hc = 50

Median: ma = 27.99659071516
Median: mb = 63.75875157706
Median: mc = 87.04551870661

Inradius: r = 7.46224976739
Circumradius: R = 75

Vertex coordinates: A[30.70108409409; 0] B[0; 0] C[86.60325403784; 50]
Centroid: CG[39.10111271065; 16.66766666667]
Coordinates of the circumscribed circle: U[15.35504204705; 73.41222918276]
Coordinates of the inscribed circle: I[27.85504204705; 7.46224976739]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 41.81103148958° = 41°48'37″ = 2.41218649974 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 168.1989685104° = 168°11'23″ = 0.20661288806 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 100 ; ; b = 75 ; ; beta = 30° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 75**2 = 100**2 + c**2 -2 * 75 * c * cos (30° ) ; ; ; ; c**2 -173.205c +4375 =0 ; ; p=1; q=-173.205080757; r=4375 ; ; D = q**2 - 4pr = 173.205**2 - 4 * 1 * 4375 = 12500 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 173.21 ± sqrt{ 12500 } }{ 2 } ; ; c_{1,2} = 86.6025403784 ± 55.9016994375 ; ; c_{1} = 142.504239816 ; ;
c_{2} = 30.7008409409 ; ; ; ; (c -142.504239816) (c -30.7008409409) = 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 = 100 ; ; b = 75 ; ; c = 30.7 ; ;

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

p = a+b+c = 100+75+30.7 = 205.7 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 205.7 }{ 2 } = 102.85 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 102.85 * (102.85-100)(102.85-75)(102.85-30.7) } ; ; T = sqrt{ 589088.52 } = 767.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 767.52 }{ 100 } = 15.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 767.52 }{ 75 } = 20.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 767.52 }{ 30.7 } = 50 ; ;

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{ 100**2-75**2-30.7**2 }{ 2 * 75 * 30.7 } ) = 138° 11'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 75**2-100**2-30.7**2 }{ 2 * 100 * 30.7 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30.7**2-100**2-75**2 }{ 2 * 75 * 100 } ) = 11° 48'37" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 767.52 }{ 102.85 } = 7.46 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 138° 11'23" } = 75 ; ;




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

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