Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=100.8549522814 and with side c=75.4522025827

#1 Acute scalene triangle.

Sides: a = 131.08   b = 97.84   c = 100.8549522814

Area: T = 4891.82875479
Perimeter: p = 329.7769522814
Semiperimeter: s = 164.8854761407

Angle ∠ A = α = 82.5422486563° = 82°32'33″ = 1.44106381633 rad
Angle ∠ B = β = 47.74° = 47°44'24″ = 0.83332201849 rad
Angle ∠ C = γ = 49.7187513437° = 49°43'3″ = 0.86877343054 rad

Height: ha = 74.63988090922
Height: hb = 99.9966474814
Height: hc = 97.01224084161

Median: ma = 74.67436521532
Median: mb = 106.2222078336
Median: mc = 104.0989670175

Inradius: r = 29.66881603937
Circumradius: R = 66.09991073688

Vertex coordinates: A[100.8549522814; 0] B[0; 0] C[88.15107743205; 97.01224084161]
Centroid: CG[633.0000990448; 32.3377469472]
Coordinates of the circumscribed circle: U[50.4254761407; 42.73768158851]
Coordinates of the inscribed circle: I[67.0454761407; 29.66881603937]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 97.4587513437° = 97°27'27″ = 1.44106381633 rad
∠ B' = β' = 132.26° = 132°15'36″ = 0.83332201849 rad
∠ C' = γ' = 130.2822486563° = 130°16'57″ = 0.86877343054 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 131.08 ; ; b = 97.84 ; ; beta = 47° 44'24" ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 97.84**2 = 131.08**2 + c**2 -2 * 131.08 * c * cos (47° 44'24") ; ; ; ; c**2 -176.302c +7609.301 =0 ; ; p=1; q=-176.302; r=7609.301 ; ; D = q**2 - 4pr = 176.302**2 - 4 * 1 * 7609.301 = 645.032853204 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 176.3 ± sqrt{ 645.03 } }{ 2 } ; ; c_{1,2} = 88.15077432 ± 12.6987484935 ; ;
c_{1} = 100.849522813 ; ; c_{2} = 75.4520258265 ; ; ; ; text{ Factored form: } ; ; (c -100.849522813) (c -75.4520258265) = 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 = 131.08 ; ; b = 97.84 ; ; c = 100.85 ; ;

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

p = a+b+c = 131.08+97.84+100.85 = 329.77 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 329.77 }{ 2 } = 164.88 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 164.88 * (164.88-131.08)(164.88-97.84)(164.88-100.85) } ; ; T = sqrt{ 23929976.76 } = 4891.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4891.83 }{ 131.08 } = 74.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4891.83 }{ 97.84 } = 100 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4891.83 }{ 100.85 } = 97.01 ; ;

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{ 97.84**2+100.85**2-131.08**2 }{ 2 * 97.84 * 100.85 } ) = 82° 32'33" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 131.08**2+100.85**2-97.84**2 }{ 2 * 131.08 * 100.85 } ) = 47° 44'24" ; ; gamma = 180° - alpha - beta = 180° - 82° 32'33" - 47° 44'24" = 49° 43'3" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4891.83 }{ 164.88 } = 29.67 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 131.08 }{ 2 * sin 82° 32'33" } = 66.1 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 97.84**2+2 * 100.85**2 - 131.08**2 } }{ 2 } = 74.674 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100.85**2+2 * 131.08**2 - 97.84**2 } }{ 2 } = 106.222 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 97.84**2+2 * 131.08**2 - 100.85**2 } }{ 2 } = 104.09 ; ;







#2 Obtuse scalene triangle.

Sides: a = 131.08   b = 97.84   c = 75.4522025827

Area: T = 3659.891137268
Perimeter: p = 304.3722025827
Semiperimeter: s = 152.1866012914

Angle ∠ A = α = 97.4587513437° = 97°27'27″ = 1.70109544903 rad
Angle ∠ B = β = 47.74° = 47°44'24″ = 0.83332201849 rad
Angle ∠ C = γ = 34.8022486563° = 34°48'9″ = 0.60774179784 rad

Height: ha = 55.84221021159
Height: hb = 74.81438056557
Height: hc = 97.01224084161

Median: ma = 57.77697611272
Median: mb = 95.10216345848
Median: mc = 109.3354642038

Inradius: r = 24.04988025319
Circumradius: R = 66.09991073688

Vertex coordinates: A[75.4522025827; 0] B[0; 0] C[88.15107743205; 97.01224084161]
Centroid: CG[54.53442667158; 32.3377469472]
Coordinates of the circumscribed circle: U[37.72660129135; 54.27655925311]
Coordinates of the inscribed circle: I[54.34660129135; 24.04988025319]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 82.5422486563° = 82°32'33″ = 1.70109544903 rad
∠ B' = β' = 132.26° = 132°15'36″ = 0.83332201849 rad
∠ C' = γ' = 145.1987513437° = 145°11'51″ = 0.60774179784 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 131.08 ; ; b = 97.84 ; ; beta = 47° 44'24" ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 97.84**2 = 131.08**2 + c**2 -2 * 131.08 * c * cos (47° 44'24") ; ; ; ; c**2 -176.302c +7609.301 =0 ; ; p=1; q=-176.302; r=7609.301 ; ; D = q**2 - 4pr = 176.302**2 - 4 * 1 * 7609.301 = 645.032853204 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 176.3 ± sqrt{ 645.03 } }{ 2 } ; ; c_{1,2} = 88.15077432 ± 12.6987484935 ; ; : Nr. 1
c_{1} = 100.849522813 ; ; c_{2} = 75.4520258265 ; ; ; ; text{ Factored form: } ; ; (c -100.849522813) (c -75.4520258265) = 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 = 131.08 ; ; b = 97.84 ; ; c = 75.45 ; ;

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

p = a+b+c = 131.08+97.84+75.45 = 304.37 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 304.37 }{ 2 } = 152.19 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 152.19 * (152.19-131.08)(152.19-97.84)(152.19-75.45) } ; ; T = sqrt{ 13394804.86 } = 3659.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3659.89 }{ 131.08 } = 55.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3659.89 }{ 97.84 } = 74.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3659.89 }{ 75.45 } = 97.01 ; ;

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{ 97.84**2+75.45**2-131.08**2 }{ 2 * 97.84 * 75.45 } ) = 97° 27'27" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 131.08**2+75.45**2-97.84**2 }{ 2 * 131.08 * 75.45 } ) = 47° 44'24" ; ; gamma = 180° - alpha - beta = 180° - 97° 27'27" - 47° 44'24" = 34° 48'9" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3659.89 }{ 152.19 } = 24.05 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 131.08 }{ 2 * sin 97° 27'27" } = 66.1 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 97.84**2+2 * 75.45**2 - 131.08**2 } }{ 2 } = 57.77 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 75.45**2+2 * 131.08**2 - 97.84**2 } }{ 2 } = 95.102 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 97.84**2+2 * 131.08**2 - 75.45**2 } }{ 2 } = 109.335 ; ;
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.