Triangle calculator SSA - result

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 271   b = 356   c = 163.7298733968

Area: T = 21173.91100927
Perimeter: p = 790.7298733968
Semiperimeter: s = 395.3644366984

Angle ∠ A = α = 46.59766386677° = 46°35'48″ = 0.81332647651 rad
Angle ∠ B = β = 107.3676666667° = 107°22' = 1.87439018402 rad
Angle ∠ C = γ = 26.03766946656° = 26°2'12″ = 0.45444260483 rad

Height: ha = 156.2655019135
Height: hb = 118.9554551083
Height: hc = 258.6466232455

Median: ma = 241.6844296477
Median: mb = 135.7944142596
Median: mc = 305.5922417148

Inradius: r = 53.5555433572
Circumradius: R = 186.502184672

Vertex coordinates: A[163.7298733968; 0] B[0; 0] C[-80.89895941205; 258.6466232455]
Centroid: CG[27.61330466159; 86.21554108182]
Coordinates of the circumscribed circle: U[81.86443669842; 167.5744354387]
Coordinates of the inscribed circle: I[39.36443669842; 53.5555433572]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.4033361332° = 133°24'12″ = 0.81332647651 rad
∠ B' = β' = 72.63333333333° = 72°38' = 1.87439018402 rad
∠ C' = γ' = 153.9633305334° = 153°57'48″ = 0.45444260483 rad

Calculate another triangle




How did we calculate this triangle?

1. Use Law of Cosines

a = 271 ; ; b = 356 ; ; beta = 107° 22' ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 356**2 = 271**2 + c**2 -2 * 271 * c * cos (107° 22') ; ; ; ; c**2 +161.779c -53295 =0 ; ; p=1; q=161.779; r=-53295 ; ; D = q**2 - 4pr = 161.779**2 - 4 * 1 * (-53295) = 239352.505748 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ -161.78 ± sqrt{ 239352.51 } }{ 2 } ; ; c_{1,2} = -80.88959412 ± 244.618328089 ; ;
c_{1} = 163.728733969 ; ; c_{2} = -325.507922209 ; ; ; ; text{ Factored form: } ; ; (c -163.728733969) (c +325.507922209) = 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 = 271 ; ; b = 356 ; ; c = 163.73 ; ;

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

p = a+b+c = 271+356+163.73 = 790.73 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 790.73 }{ 2 } = 395.36 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 395.36 * (395.36-271)(395.36-356)(395.36-163.73) } ; ; T = sqrt{ 448334468.62 } = 21173.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21173.91 }{ 271 } = 156.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21173.91 }{ 356 } = 118.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21173.91 }{ 163.73 } = 258.65 ; ;

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{ 356**2+163.73**2-271**2 }{ 2 * 356 * 163.73 } ) = 46° 35'48" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 271**2+163.73**2-356**2 }{ 2 * 271 * 163.73 } ) = 107° 22' ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 271**2+356**2-163.73**2 }{ 2 * 271 * 356 } ) = 26° 2'12" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21173.91 }{ 395.36 } = 53.56 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 271 }{ 2 * sin 46° 35'48" } = 186.5 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 356**2+2 * 163.73**2 - 271**2 } }{ 2 } = 241.684 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 163.73**2+2 * 271**2 - 356**2 } }{ 2 } = 135.794 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 356**2+2 * 271**2 - 163.73**2 } }{ 2 } = 305.592 ; ;
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.