Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=127.7477345809 and with side c=57.38332665842

#1 Acute scalene triangle.

Sides: a = 118   b = 81.2   c = 127.7477345809

Area: T = 4674.42988628
Perimeter: p = 326.9477345809
Semiperimeter: s = 163.4743672905

Angle ∠ A = α = 64.32443340369° = 64°19'28″ = 1.12326714181 rad
Angle ∠ B = β = 38.33° = 38°19'48″ = 0.66989847023 rad
Angle ∠ C = γ = 77.34656659631° = 77°20'44″ = 1.35499365332 rad

Height: ha = 79.22876078441
Height: hb = 115.1343715833
Height: hc = 73.18224028623

Median: ma = 89.30551632363
Median: mb = 116.0754683634
Median: mc = 78.60658134597

Inradius: r = 28.59443833019
Circumradius: R = 65.46438248079

Vertex coordinates: A[127.7477345809; 0] B[0; 0] C[92.56553061968; 73.18224028623]
Centroid: CG[73.43875506687; 24.39441342874]
Coordinates of the circumscribed circle: U[63.87436729047; 14.34110692819]
Coordinates of the inscribed circle: I[82.27436729047; 28.59443833019]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.6765665963° = 115°40'32″ = 1.12326714181 rad
∠ B' = β' = 141.67° = 141°40'12″ = 0.66989847023 rad
∠ C' = γ' = 102.6544334037° = 102°39'16″ = 1.35499365332 rad


How did we calculate this triangle?

1. Use Law of Cosines

a = 118 ; ; b = 81.2 ; ; beta = 38° 19'48" ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 81.2**2 = 118**2 + c**2 -2 * 118 * c * cos (38° 19'48") ; ; ; ; c**2 -185.131c +7330.56 =0 ; ; p=1; q=-185.131; r=7330.56 ; ; D = q**2 - 4pr = 185.131**2 - 4 * 1 * 7330.56 = 4951.10364521 ; ;
D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 185.13 ± sqrt{ 4951.1 } }{ 2 } ; ; c_{1,2} = 92.5653062 ± 35.1820396126 ; ; c_{1} = 127.747345809 ; ; c_{2} = 57.3832665842 ; ; ; ; text{ Factored form: } ; ; (c -127.747345809) (c -57.3832665842) = 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 = 118 ; ; b = 81.2 ; ; c = 127.75 ; ;

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

p = a+b+c = 118+81.2+127.75 = 326.95 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 326.95 }{ 2 } = 163.47 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 163.47 * (163.47-118)(163.47-81.2)(163.47-127.75) } ; ; T = sqrt{ 21850285.19 } = 4674.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4674.43 }{ 118 } = 79.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4674.43 }{ 81.2 } = 115.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4674.43 }{ 127.75 } = 73.18 ; ;

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{ 81.2**2+127.75**2-118**2 }{ 2 * 81.2 * 127.75 } ) = 64° 19'28" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 118**2+127.75**2-81.2**2 }{ 2 * 118 * 127.75 } ) = 38° 19'48" ; ;
 gamma = 180° - alpha - beta = 180° - 64° 19'28" - 38° 19'48" = 77° 20'44" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4674.43 }{ 163.47 } = 28.59 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 118 }{ 2 * sin 64° 19'28" } = 65.46 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 81.2**2+2 * 127.75**2 - 118**2 } }{ 2 } = 89.305 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 127.75**2+2 * 118**2 - 81.2**2 } }{ 2 } = 116.075 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 81.2**2+2 * 118**2 - 127.75**2 } }{ 2 } = 78.606 ; ;



#2 Obtuse scalene triangle.

Sides: a = 118   b = 81.2   c = 57.38332665842

Area: T = 2099.723266636
Perimeter: p = 256.5833266584
Semiperimeter: s = 128.2921633292

Angle ∠ A = α = 115.6765665963° = 115°40'32″ = 2.01989212355 rad
Angle ∠ B = β = 38.33° = 38°19'48″ = 0.66989847023 rad
Angle ∠ C = γ = 25.99443340369° = 25°59'40″ = 0.45436867158 rad

Height: ha = 35.58985197688
Height: hb = 51.71773070532
Height: hc = 73.18224028623

Median: ma = 38.2387934593
Median: mb = 83.42769719092
Median: mc = 97.13765542884

Inradius: r = 16.36767934726
Circumradius: R = 65.46438248079

Vertex coordinates: A[57.38332665842; 0] B[0; 0] C[92.56553061968; 73.18224028623]
Centroid: CG[49.98328575936; 24.39441342874]
Coordinates of the circumscribed circle: U[28.69216332921; 58.84113335804]
Coordinates of the inscribed circle: I[47.09216332921; 16.36767934726]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 64.32443340369° = 64°19'28″ = 2.01989212355 rad
∠ B' = β' = 141.67° = 141°40'12″ = 0.66989847023 rad
∠ C' = γ' = 154.0065665963° = 154°20″ = 0.45436867158 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 118 ; ; b = 81.2 ; ; beta = 38° 19'48" ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 81.2**2 = 118**2 + c**2 -2 * 118 * c * cos (38° 19'48") ; ; ; ; c**2 -185.131c +7330.56 =0 ; ; p=1; q=-185.131; r=7330.56 ; ; D = q**2 - 4pr = 185.131**2 - 4 * 1 * 7330.56 = 4951.10364521 ; ; : Nr. 1
D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 185.13 ± sqrt{ 4951.1 } }{ 2 } ; ; c_{1,2} = 92.5653062 ± 35.1820396126 ; ; c_{1} = 127.747345809 ; ; c_{2} = 57.3832665842 ; ; ; ; text{ Factored form: } ; ; (c -127.747345809) (c -57.3832665842) = 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 = 118 ; ; b = 81.2 ; ; c = 57.38 ; ;

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

p = a+b+c = 118+81.2+57.38 = 256.58 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 256.58 }{ 2 } = 128.29 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 128.29 * (128.29-118)(128.29-81.2)(128.29-57.38) } ; ; T = sqrt{ 4408835.28 } = 2099.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2099.72 }{ 118 } = 35.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2099.72 }{ 81.2 } = 51.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2099.72 }{ 57.38 } = 73.18 ; ;

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{ 81.2**2+57.38**2-118**2 }{ 2 * 81.2 * 57.38 } ) = 115° 40'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 118**2+57.38**2-81.2**2 }{ 2 * 118 * 57.38 } ) = 38° 19'48" ; ;
 gamma = 180° - alpha - beta = 180° - 115° 40'32" - 38° 19'48" = 25° 59'40" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2099.72 }{ 128.29 } = 16.37 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 118 }{ 2 * sin 115° 40'32" } = 65.46 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 81.2**2+2 * 57.38**2 - 118**2 } }{ 2 } = 38.238 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 57.38**2+2 * 118**2 - 81.2**2 } }{ 2 } = 83.427 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 81.2**2+2 * 118**2 - 57.38**2 } }{ 2 } = 97.137 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.