Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=12.79436569493 and with side c=1.36328706842

#1 Obtuse scalene triangle.

Sides: a = 7.81   b = 6.6   c = 12.79436569493

Area: T = 21.11436831041
Perimeter: p = 27.20436569493
Semiperimeter: s = 13.60218284747

Angle ∠ A = α = 30.00765021269° = 30°23″ = 0.52437122591 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 124.9933497873° = 124°59'37″ = 2.18215480815 rad

Height: ha = 5.40768330612
Height: hb = 6.39880857891
Height: hc = 3.30106486242

Median: ma = 9.40105214785
Median: mb = 10.07220841472
Median: mc = 3.37702574777

Inradius: r = 1.55222680016
Circumradius: R = 7.80884652244

Vertex coordinates: A[12.79436569493; 0] B[0; 0] C[7.07882638168; 3.30106486242]
Centroid: CG[6.62439735887; 1.11002162081]
Coordinates of the circumscribed circle: U[6.39768284747; -4.4788025751]
Coordinates of the inscribed circle: I[7.00218284747; 1.55222680016]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.9933497873° = 149°59'37″ = 0.52437122591 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 55.00765021269° = 55°23″ = 2.18215480815 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 7.81 ; ; b = 6.6 ; ; beta = 25° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 6.6**2 = 7.81**2 + c**2 -2 * 7.81 * c * cos (25° ) ; ; ; ; c**2 -14.157c +17.436 =0 ; ; p=1; q=-14.157; r=17.436 ; ; D = q**2 - 4pr = 14.157**2 - 4 * 1 * 17.436 = 130.662874638 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 14.16 ± sqrt{ 130.66 } }{ 2 } ; ; c_{1,2} = 7.07826382 ± 5.71539313255 ; ; c_{1} = 12.7936569526 ; ; c_{2} = 1.36287068745 ; ; ; ; text{ Factored form: } ; ; (c -12.7936569526) (c -1.36287068745) = 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 = 7.81 ; ; b = 6.6 ; ; c = 12.79 ; ;

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

p = a+b+c = 7.81+6.6+12.79 = 27.2 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.2 }{ 2 } = 13.6 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.6 * (13.6-7.81)(13.6-6.6)(13.6-12.79) } ; ; T = sqrt{ 445.79 } = 21.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.11 }{ 7.81 } = 5.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.11 }{ 6.6 } = 6.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.11 }{ 12.79 } = 3.3 ; ;

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{ 6.6**2+12.79**2-7.81**2 }{ 2 * 6.6 * 12.79 } ) = 30° 23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.81**2+12.79**2-6.6**2 }{ 2 * 7.81 * 12.79 } ) = 25° ; ; gamma = 180° - alpha - beta = 180° - 30° 23" - 25° = 124° 59'37" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.11 }{ 13.6 } = 1.55 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.81 }{ 2 * sin 30° 23" } = 7.81 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.6**2+2 * 12.79**2 - 7.81**2 } }{ 2 } = 9.401 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.79**2+2 * 7.81**2 - 6.6**2 } }{ 2 } = 10.072 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.6**2+2 * 7.81**2 - 12.79**2 } }{ 2 } = 3.37 ; ;







#2 Obtuse scalene triangle.

Sides: a = 7.81   b = 6.6   c = 1.36328706842

Area: T = 2.24991786244
Perimeter: p = 15.77328706842
Semiperimeter: s = 7.88664353421

Angle ∠ A = α = 149.9933497873° = 149°59'37″ = 2.61878803945 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 5.00765021269° = 5°23″ = 0.08773799461 rad

Height: ha = 0.57659740395
Height: hb = 0.68215692801
Height: hc = 3.30106486242

Median: ma = 2.73112420711
Median: mb = 4.53217500208
Median: mc = 7.19881730928

Inradius: r = 0.28551958492
Circumradius: R = 7.80884652244

Vertex coordinates: A[1.36328706842; 0] B[0; 0] C[7.07882638168; 3.30106486242]
Centroid: CG[2.81437115003; 1.11002162081]
Coordinates of the circumscribed circle: U[0.68114353421; 7.77986743752]
Coordinates of the inscribed circle: I[1.28664353421; 0.28551958492]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.00765021269° = 30°23″ = 2.61878803945 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 174.9933497873° = 174°59'37″ = 0.08773799461 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 7.81 ; ; b = 6.6 ; ; beta = 25° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 6.6**2 = 7.81**2 + c**2 -2 * 7.81 * c * cos (25° ) ; ; ; ; c**2 -14.157c +17.436 =0 ; ; p=1; q=-14.157; r=17.436 ; ; D = q**2 - 4pr = 14.157**2 - 4 * 1 * 17.436 = 130.662874638 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 14.16 ± sqrt{ 130.66 } }{ 2 } ; ; c_{1,2} = 7.07826382 ± 5.71539313255 ; ; c_{1} = 12.7936569526 ; ; c_{2} = 1.36287068745 ; ; ; ; text{ Factored form: } ; ; (c -12.7936569526) (c -1.36287068745) = 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 = 7.81 ; ; b = 6.6 ; ; c = 1.36 ; ;

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

p = a+b+c = 7.81+6.6+1.36 = 15.77 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.77 }{ 2 } = 7.89 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.89 * (7.89-7.81)(7.89-6.6)(7.89-1.36) } ; ; T = sqrt{ 5.06 } = 2.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.25 }{ 7.81 } = 0.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.25 }{ 6.6 } = 0.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.25 }{ 1.36 } = 3.3 ; ;

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{ 6.6**2+1.36**2-7.81**2 }{ 2 * 6.6 * 1.36 } ) = 149° 59'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.81**2+1.36**2-6.6**2 }{ 2 * 7.81 * 1.36 } ) = 25° ; ; gamma = 180° - alpha - beta = 180° - 149° 59'37" - 25° = 5° 23" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.25 }{ 7.89 } = 0.29 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.81 }{ 2 * sin 149° 59'37" } = 7.81 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.6**2+2 * 1.36**2 - 7.81**2 } }{ 2 } = 2.731 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.36**2+2 * 7.81**2 - 6.6**2 } }{ 2 } = 4.532 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.6**2+2 * 7.81**2 - 1.36**2 } }{ 2 } = 7.198 ; ;
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.