Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=63.77107838668 and with side c=10.29326443773

#1 Obtuse scalene triangle.

Sides: a = 38.1   b = 28.2   c = 63.77107838668

Area: T = 285.6598500424
Perimeter: p = 130.0710783867
Semiperimeter: s = 65.03553919334

Angle ∠ A = α = 18.52334043434° = 18°31'24″ = 0.32332943945 rad
Angle ∠ B = β = 13.6° = 13°36' = 0.23773647783 rad
Angle ∠ C = γ = 147.8776595657° = 147°52'36″ = 2.58109334808 rad

Height: ha = 14.99551968727
Height: hb = 20.25994681152
Height: hc = 8.95989145092

Median: ma = 45.47660809382
Median: mb = 50.65999153902
Median: mc = 10.33218333926

Inradius: r = 4.39223545616
Circumradius: R = 59.96437377327

Vertex coordinates: A[63.77107838668; 0] B[0; 0] C[37.0321714122; 8.95989145092]
Centroid: CG[33.6010832663; 2.98663048364]
Coordinates of the circumscribed circle: U[31.88553919334; -50.78435763228]
Coordinates of the inscribed circle: I[36.83553919334; 4.39223545616]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.4776595657° = 161°28'36″ = 0.32332943945 rad
∠ B' = β' = 166.4° = 166°24' = 0.23773647783 rad
∠ C' = γ' = 32.12334043434° = 32°7'24″ = 2.58109334808 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 = 38.1 ; ; b = 28.2 ; ; c = 63.77 ; ;

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

p = a+b+c = 38.1+28.2+63.77 = 130.07 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 130.07 }{ 2 } = 65.04 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 65.04 * (65.04-38.1)(65.04-28.2)(65.04-63.77) } ; ; T = sqrt{ 81600.78 } = 285.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 285.66 }{ 38.1 } = 15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 285.66 }{ 28.2 } = 20.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 285.66 }{ 63.77 } = 8.96 ; ;

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{ 38.1**2-28.2**2-63.77**2 }{ 2 * 28.2 * 63.77 } ) = 18° 31'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28.2**2-38.1**2-63.77**2 }{ 2 * 38.1 * 63.77 } ) = 13° 36' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 63.77**2-38.1**2-28.2**2 }{ 2 * 28.2 * 38.1 } ) = 147° 52'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 285.66 }{ 65.04 } = 4.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38.1 }{ 2 * sin 18° 31'24" } = 59.96 ; ;





#2 Obtuse scalene triangle.

Sides: a = 38.1   b = 28.2   c = 10.29326443773

Area: T = 46.10554605248
Perimeter: p = 76.59326443773
Semiperimeter: s = 38.29663221886

Angle ∠ A = α = 161.4776595657° = 161°28'36″ = 2.81882982591 rad
Angle ∠ B = β = 13.6° = 13°36' = 0.23773647783 rad
Angle ∠ C = γ = 4.92334043434° = 4°55'24″ = 0.08659296162 rad

Height: ha = 2.42202341483
Height: hb = 3.27698908174
Height: hc = 8.95989145092

Median: ma = 9.36441211087
Median: mb = 24.08224472207
Median: mc = 33.12200900955

Inradius: r = 1.20439135324
Circumradius: R = 59.96437377327

Vertex coordinates: A[10.29326443773; 0] B[0; 0] C[37.0321714122; 8.95989145092]
Centroid: CG[15.77547861664; 2.98663048364]
Coordinates of the circumscribed circle: U[5.14663221886; 59.7422490832]
Coordinates of the inscribed circle: I[10.09663221886; 1.20439135324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 18.52334043434° = 18°31'24″ = 2.81882982591 rad
∠ B' = β' = 166.4° = 166°24' = 0.23773647783 rad
∠ C' = γ' = 175.0776595657° = 175°4'36″ = 0.08659296162 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 38.1 ; ; b = 28.2 ; ; beta = 13° 36' ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 28.2**2 = 38.1**2 + c**2 -2 * 28.2 * c * cos (13° 36') ; ; ; ; c**2 -74.063c +656.37 =0 ; ; p=1; q=-74.0634282441; r=656.37 ; ; D = q**2 - 4pr = 74.063**2 - 4 * 1 * 656.37 = 2859.91140327 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 74.06 ± sqrt{ 2859.91 } }{ 2 } ; ; c_{1,2} = 37.031714122 ± 26.7390697448 ; ;
c_{1} = 63.7707838668 ; ; c_{2} = 10.2926443773 ; ; ; ; (c -63.7707838668) (c -10.2926443773) = 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 = 38.1 ; ; b = 28.2 ; ; c = 10.29 ; ;

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

p = a+b+c = 38.1+28.2+10.29 = 76.59 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76.59 }{ 2 } = 38.3 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.3 * (38.3-38.1)(38.3-28.2)(38.3-10.29) } ; ; T = sqrt{ 2125.71 } = 46.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.11 }{ 38.1 } = 2.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.11 }{ 28.2 } = 3.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.11 }{ 10.29 } = 8.96 ; ;

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{ 38.1**2-28.2**2-10.29**2 }{ 2 * 28.2 * 10.29 } ) = 161° 28'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28.2**2-38.1**2-10.29**2 }{ 2 * 38.1 * 10.29 } ) = 13° 36' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.29**2-38.1**2-28.2**2 }{ 2 * 28.2 * 38.1 } ) = 4° 55'24" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.11 }{ 38.3 } = 1.2 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38.1 }{ 2 * sin 161° 28'36" } = 59.96 ; ;




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

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