Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=28.55661452939 and with side c=17.56604058195

#1 Obtuse scalene triangle.

Sides: a = 23.6   b = 7.45   c = 28.55661452939

Area: T = 71.78332546173
Perimeter: p = 59.60661452939
Semiperimeter: s = 29.80330726469

Angle ∠ A = α = 42.44113004475° = 42°26'29″ = 0.74107404316 rad
Angle ∠ B = β = 12.3° = 12°18' = 0.2154675498 rad
Angle ∠ C = γ = 125.2598699552° = 125°15'31″ = 2.1866176724 rad

Height: ha = 6.08333266625
Height: hb = 19.27106723805
Height: hc = 5.02875171161

Median: ma = 17.21215649208
Median: mb = 25.92993480833
Median: mc = 10.11877018877

Inradius: r = 2.40985857008
Circumradius: R = 17.48657684161

Vertex coordinates: A[28.55661452939; 0] B[0; 0] C[23.05882755567; 5.02875171161]
Centroid: CG[17.20548069502; 1.67658390387]
Coordinates of the circumscribed circle: U[14.27880726469; -10.09439951749]
Coordinates of the inscribed circle: I[22.35330726469; 2.40985857008]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.5598699552° = 137°33'31″ = 0.74107404316 rad
∠ B' = β' = 167.7° = 167°42' = 0.2154675498 rad
∠ C' = γ' = 54.74113004475° = 54°44'29″ = 2.1866176724 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 = 23.6 ; ; b = 7.45 ; ; c = 28.56 ; ;

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

p = a+b+c = 23.6+7.45+28.56 = 59.61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59.61 }{ 2 } = 29.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.8 * (29.8-23.6)(29.8-7.45)(29.8-28.56) } ; ; T = sqrt{ 5152.84 } = 71.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.78 }{ 23.6 } = 6.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.78 }{ 7.45 } = 19.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.78 }{ 28.56 } = 5.03 ; ;

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{ 23.6**2-7.45**2-28.56**2 }{ 2 * 7.45 * 28.56 } ) = 42° 26'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.45**2-23.6**2-28.56**2 }{ 2 * 23.6 * 28.56 } ) = 12° 18' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28.56**2-23.6**2-7.45**2 }{ 2 * 7.45 * 23.6 } ) = 125° 15'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.78 }{ 29.8 } = 2.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23.6 }{ 2 * sin 42° 26'29" } = 17.49 ; ;





#2 Obtuse scalene triangle.

Sides: a = 23.6   b = 7.45   c = 17.56604058195

Area: T = 44.14326204114
Perimeter: p = 48.61104058195
Semiperimeter: s = 24.30552029097

Angle ∠ A = α = 137.5598699552° = 137°33'31″ = 2.4010852222 rad
Angle ∠ B = β = 12.3° = 12°18' = 0.2154675498 rad
Angle ∠ C = γ = 30.14113004475° = 30°8'29″ = 0.52660649336 rad

Height: ha = 3.74109000349
Height: hb = 11.85503678957
Height: hc = 5.02875171161

Median: ma = 6.5344154595
Median: mb = 20.46443177573
Median: mc = 15.13773474184

Inradius: r = 1.81661798762
Circumradius: R = 17.48657684161

Vertex coordinates: A[17.56604058195; 0] B[0; 0] C[23.05882755567; 5.02875171161]
Centroid: CG[13.54395604587; 1.67658390387]
Coordinates of the circumscribed circle: U[8.78802029097; 15.1221512291]
Coordinates of the inscribed circle: I[16.85552029097; 1.81661798762]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.44113004475° = 42°26'29″ = 2.4010852222 rad
∠ B' = β' = 167.7° = 167°42' = 0.2154675498 rad
∠ C' = γ' = 149.8598699552° = 149°51'31″ = 0.52660649336 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 23.6 ; ; b = 7.45 ; ; beta = 12° 18' ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 7.45**2 = 23.6**2 + c**2 -2 * 7.45 * c * cos (12° 18') ; ; ; ; c**2 -46.117c +501.458 =0 ; ; p=1; q=-46.1165511133; r=501.4575 ; ; D = q**2 - 4pr = 46.117**2 - 4 * 1 * 501.458 = 120.90628659 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 46.12 ± sqrt{ 120.91 } }{ 2 } ; ; c_{1,2} = 23.0582755567 ± 5.49786973722 ; ;
c_{1} = 28.5561452939 ; ; c_{2} = 17.5604058195 ; ; ; ; (c -28.5561452939) (c -17.5604058195) = 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 = 23.6 ; ; b = 7.45 ; ; c = 17.56 ; ;

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

p = a+b+c = 23.6+7.45+17.56 = 48.61 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48.61 }{ 2 } = 24.31 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.31 * (24.31-23.6)(24.31-7.45)(24.31-17.56) } ; ; T = sqrt{ 1948.57 } = 44.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.14 }{ 23.6 } = 3.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.14 }{ 7.45 } = 11.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.14 }{ 17.56 } = 5.03 ; ;

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{ 23.6**2-7.45**2-17.56**2 }{ 2 * 7.45 * 17.56 } ) = 137° 33'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.45**2-23.6**2-17.56**2 }{ 2 * 23.6 * 17.56 } ) = 12° 18' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17.56**2-23.6**2-7.45**2 }{ 2 * 7.45 * 23.6 } ) = 30° 8'29" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.14 }{ 24.31 } = 1.82 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23.6 }{ 2 * sin 137° 33'31" } = 17.49 ; ;




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

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