Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=103.2921895057 and with side c=11.5898518144

#1 Obtuse scalene triangle.

Sides: a = 71   b = 62   c = 103.2921895057

Area: T = 2155.328756716
Perimeter: p = 236.2921895057
Semiperimeter: s = 118.1465947529

Angle ∠ A = α = 42.30774684462° = 42°18'27″ = 0.73884046226 rad
Angle ∠ B = β = 36° = 0.62883185307 rad
Angle ∠ C = γ = 101.6932531554° = 101°41'33″ = 1.77548695003 rad

Height: ha = 60.7133452596
Height: hb = 69.52766957148
Height: hc = 41.73327529128

Median: ma = 77.43661530053
Median: mb = 83.03107641315
Median: mc = 42.13330761264

Inradius: r = 18.24329242157
Circumradius: R = 52.74403501178

Vertex coordinates: A[103.2921895057; 0] B[0; 0] C[57.44402066006; 41.73327529128]
Centroid: CG[53.57773672193; 13.91109176376]
Coordinates of the circumscribed circle: U[51.64659475286; -10.6888341051]
Coordinates of the inscribed circle: I[56.14659475286; 18.24329242157]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.6932531554° = 137°41'33″ = 0.73884046226 rad
∠ B' = β' = 144° = 0.62883185307 rad
∠ C' = γ' = 78.30774684462° = 78°18'27″ = 1.77548695003 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 = 71 ; ; b = 62 ; ; c = 103.29 ; ;

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

p = a+b+c = 71+62+103.29 = 236.29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 236.29 }{ 2 } = 118.15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 118.15 * (118.15-71)(118.15-62)(118.15-103.29) } ; ; T = sqrt{ 4645436.92 } = 2155.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2155.33 }{ 71 } = 60.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2155.33 }{ 62 } = 69.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2155.33 }{ 103.29 } = 41.73 ; ;

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{ 71**2-62**2-103.29**2 }{ 2 * 62 * 103.29 } ) = 42° 18'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 62**2-71**2-103.29**2 }{ 2 * 71 * 103.29 } ) = 36° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 103.29**2-71**2-62**2 }{ 2 * 62 * 71 } ) = 101° 41'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2155.33 }{ 118.15 } = 18.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 71 }{ 2 * sin 42° 18'27" } = 52.74 ; ;





#2 Obtuse scalene triangle.

Sides: a = 71   b = 62   c = 11.5898518144

Area: T = 241.8110382165
Perimeter: p = 144.5898518144
Semiperimeter: s = 72.2944259072

Angle ∠ A = α = 137.6932531554° = 137°41'33″ = 2.4033188031 rad
Angle ∠ B = β = 36° = 0.62883185307 rad
Angle ∠ C = γ = 6.30774684462° = 6°18'27″ = 0.11100860919 rad

Height: ha = 6.8121560061
Height: hb = 7.88003349085
Height: hc = 41.73327529128

Median: ma = 26.99880902359
Median: mb = 40.33217105562
Median: mc = 66.43997482059

Inradius: r = 3.34548075306
Circumradius: R = 52.74403501178

Vertex coordinates: A[11.5898518144; 0] B[0; 0] C[57.44402066006; 41.73327529128]
Centroid: CG[23.01095749149; 13.91109176376]
Coordinates of the circumscribed circle: U[5.7944259072; 52.42110939638]
Coordinates of the inscribed circle: I[10.2944259072; 3.34548075306]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.30774684462° = 42°18'27″ = 2.4033188031 rad
∠ B' = β' = 144° = 0.62883185307 rad
∠ C' = γ' = 173.6932531554° = 173°41'33″ = 0.11100860919 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 71 ; ; b = 62 ; ; beta = 36° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 62**2 = 71**2 + c**2 -2 * 62 * c * cos (36° ) ; ; ; ; c**2 -114.88c +1197 =0 ; ; p=1; q=-114.880413201; r=1197 ; ; D = q**2 - 4pr = 114.88**2 - 4 * 1 * 1197 = 8409.50933729 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 114.88 ± sqrt{ 8409.51 } }{ 2 } ; ; c_{1,2} = 57.4402066006 ± 45.8516884566 ; ; c_{1} = 103.291895057 ; ;
c_{2} = 11.588518144 ; ; ; ; (c -103.291895057) (c -11.588518144) = 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 = 71 ; ; b = 62 ; ; c = 11.59 ; ;

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

p = a+b+c = 71+62+11.59 = 144.59 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 144.59 }{ 2 } = 72.29 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72.29 * (72.29-71)(72.29-62)(72.29-11.59) } ; ; T = sqrt{ 58472.26 } = 241.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 241.81 }{ 71 } = 6.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 241.81 }{ 62 } = 7.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 241.81 }{ 11.59 } = 41.73 ; ;

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{ 71**2-62**2-11.59**2 }{ 2 * 62 * 11.59 } ) = 137° 41'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 62**2-71**2-11.59**2 }{ 2 * 71 * 11.59 } ) = 36° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.59**2-71**2-62**2 }{ 2 * 62 * 71 } ) = 6° 18'27" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 241.81 }{ 72.29 } = 3.34 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 71 }{ 2 * sin 137° 41'33" } = 52.74 ; ;




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

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