Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=61.468776017 and with side c=28.38548784334

#1 Obtuse scalene triangle.

Sides: a = 45.93   b = 19.1   c = 61.468776017

Area: T = 293.4989621489
Perimeter: p = 126.498776017
Semiperimeter: s = 63.2498880085

Angle ∠ A = α = 29.99878661524° = 29°59'52″ = 0.52435615329 rad
Angle ∠ B = β = 12° = 0.20994395102 rad
Angle ∠ C = γ = 138.0022133848° = 138°8″ = 2.40985916104 rad

Height: ha = 12.78798659477
Height: hb = 30.73218975382
Height: hc = 9.54993839593

Median: ma = 39.2965757343
Median: mb = 53.41108857833
Median: mc = 17.1066024229

Inradius: r = 4.64402342792
Circumradius: R = 45.93329629923

Vertex coordinates: A[61.468776017; 0] B[0; 0] C[44.92663193017; 9.54993839593]
Centroid: CG[35.46546931572; 3.18331279864]
Coordinates of the circumscribed circle: U[30.7343880085; -34.13659884019]
Coordinates of the inscribed circle: I[44.1498880085; 4.64402342792]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0022133848° = 150°8″ = 0.52435615329 rad
∠ B' = β' = 168° = 0.20994395102 rad
∠ C' = γ' = 41.99878661524° = 41°59'52″ = 2.40985916104 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 45.93 ; ; b = 19.1 ; ; beta = 12° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 19.1**2 = 45.93**2 + c**2 -2 * 45.93 * c * cos (12° ) ; ; ; ; c**2 -89.853c +1744.755 =0 ; ; p=1; q=-89.853; r=1744.755 ; ; D = q**2 - 4pr = 89.853**2 - 4 * 1 * 1744.755 = 1094.47706399 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 89.85 ± sqrt{ 1094.48 } }{ 2 } ; ; c_{1,2} = 44.9263193 ± 16.5414408683 ; ;
c_{1} = 61.4677601683 ; ; c_{2} = 28.3848784317 ; ; ; ; text{ Factored form: } ; ; (c -61.4677601683) (c -28.3848784317) = 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 = 45.93 ; ; b = 19.1 ; ; c = 61.47 ; ;

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

p = a+b+c = 45.93+19.1+61.47 = 126.5 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 126.5 }{ 2 } = 63.25 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 63.25 * (63.25-45.93)(63.25-19.1)(63.25-61.47) } ; ; T = sqrt{ 86136.16 } = 293.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 293.49 }{ 45.93 } = 12.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 293.49 }{ 19.1 } = 30.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 293.49 }{ 61.47 } = 9.55 ; ;

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{ 19.1**2+61.47**2-45.93**2 }{ 2 * 19.1 * 61.47 } ) = 29° 59'52" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 45.93**2+61.47**2-19.1**2 }{ 2 * 45.93 * 61.47 } ) = 12° ; ; gamma = 180° - alpha - beta = 180° - 29° 59'52" - 12° = 138° 8" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 293.49 }{ 63.25 } = 4.64 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 45.93 }{ 2 * sin 29° 59'52" } = 45.93 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.1**2+2 * 61.47**2 - 45.93**2 } }{ 2 } = 39.296 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 61.47**2+2 * 45.93**2 - 19.1**2 } }{ 2 } = 53.411 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.1**2+2 * 45.93**2 - 61.47**2 } }{ 2 } = 17.106 ; ;







#2 Obtuse scalene triangle.

Sides: a = 45.93   b = 19.1   c = 28.38548784334

Area: T = 135.5299051399
Perimeter: p = 93.41548784334
Semiperimeter: s = 46.70774392167

Angle ∠ A = α = 150.0022133848° = 150°8″ = 2.61880311207 rad
Angle ∠ B = β = 12° = 0.20994395102 rad
Angle ∠ C = γ = 17.99878661524° = 17°59'52″ = 0.31441220227 rad

Height: ha = 5.90215480688
Height: hb = 14.19215237067
Height: hc = 9.54993839593

Median: ma = 7.60768677417
Median: mb = 36.96552622315
Median: mc = 32.18332583664

Inradius: r = 2.90216587865
Circumradius: R = 45.93329629923

Vertex coordinates: A[28.38548784334; 0] B[0; 0] C[44.92663193017; 9.54993839593]
Centroid: CG[24.43770659117; 3.18331279864]
Coordinates of the circumscribed circle: U[14.19224392167; 43.68553723612]
Coordinates of the inscribed circle: I[27.60774392167; 2.90216587865]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.99878661524° = 29°59'52″ = 2.61880311207 rad
∠ B' = β' = 168° = 0.20994395102 rad
∠ C' = γ' = 162.0022133848° = 162°8″ = 0.31441220227 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 45.93 ; ; b = 19.1 ; ; beta = 12° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 19.1**2 = 45.93**2 + c**2 -2 * 45.93 * c * cos (12° ) ; ; ; ; c**2 -89.853c +1744.755 =0 ; ; p=1; q=-89.853; r=1744.755 ; ; D = q**2 - 4pr = 89.853**2 - 4 * 1 * 1744.755 = 1094.47706399 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 89.85 ± sqrt{ 1094.48 } }{ 2 } ; ; c_{1,2} = 44.9263193 ± 16.5414408683 ; ; : Nr. 1
c_{1} = 61.4677601683 ; ; c_{2} = 28.3848784317 ; ; ; ; text{ Factored form: } ; ; (c -61.4677601683) (c -28.3848784317) = 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 = 45.93 ; ; b = 19.1 ; ; c = 28.38 ; ;

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

p = a+b+c = 45.93+19.1+28.38 = 93.41 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 93.41 }{ 2 } = 46.71 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 46.71 * (46.71-45.93)(46.71-19.1)(46.71-28.38) } ; ; T = sqrt{ 18368.12 } = 135.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.53 }{ 45.93 } = 5.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.53 }{ 19.1 } = 14.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.53 }{ 28.38 } = 9.55 ; ;

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{ 19.1**2+28.38**2-45.93**2 }{ 2 * 19.1 * 28.38 } ) = 150° 8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 45.93**2+28.38**2-19.1**2 }{ 2 * 45.93 * 28.38 } ) = 12° ; ; gamma = 180° - alpha - beta = 180° - 150° 8" - 12° = 17° 59'52" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.53 }{ 46.71 } = 2.9 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 45.93 }{ 2 * sin 150° 8" } = 45.93 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.1**2+2 * 28.38**2 - 45.93**2 } }{ 2 } = 7.607 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28.38**2+2 * 45.93**2 - 19.1**2 } }{ 2 } = 36.965 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.1**2+2 * 45.93**2 - 28.38**2 } }{ 2 } = 32.183 ; ;
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.