Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=50.95440389941 and with side c=2.66990720242

#1 Obtuse scalene triangle.

Sides: a = 35   b = 33   c = 50.95440389941

Area: T = 573.1710936256
Perimeter: p = 118.9544038994
Semiperimeter: s = 59.47770194971

Angle ∠ A = α = 42.98801101602° = 42°58'48″ = 0.75501444352 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 97.02198898398° = 97°1'12″ = 1.69333165176 rad

Height: ha = 32.75326249289
Height: hb = 34.73876325003
Height: hc = 22.4987566339

Median: ma = 39.19770285214
Median: mb = 40.47772410733
Median: mc = 22.53771133366

Inradius: r = 9.6376846989
Circumradius: R = 25.66994431432

Vertex coordinates: A[50.95440389941; 0] B[0; 0] C[26.81215555092; 22.4987566339]
Centroid: CG[25.92218648344; 7.49991887797]
Coordinates of the circumscribed circle: U[25.47770194971; -3.13771625442]
Coordinates of the inscribed circle: I[26.47770194971; 9.6376846989]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.021988984° = 137°1'12″ = 0.75501444352 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 82.98801101602° = 82°58'48″ = 1.69333165176 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 = 35 ; ; b = 33 ; ; c = 50.95 ; ;

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

p = a+b+c = 35+33+50.95 = 118.95 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 118.95 }{ 2 } = 59.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59.48 * (59.48-35)(59.48-33)(59.48-50.95) } ; ; T = sqrt{ 328524.92 } = 573.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 573.17 }{ 35 } = 32.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 573.17 }{ 33 } = 34.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 573.17 }{ 50.95 } = 22.5 ; ;

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{ 35**2-33**2-50.95**2 }{ 2 * 33 * 50.95 } ) = 42° 58'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 33**2-35**2-50.95**2 }{ 2 * 35 * 50.95 } ) = 40° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 50.95**2-35**2-33**2 }{ 2 * 33 * 35 } ) = 97° 1'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 573.17 }{ 59.48 } = 9.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 35 }{ 2 * sin 42° 58'48" } = 25.67 ; ;





#2 Obtuse scalene triangle.

Sides: a = 35   b = 33   c = 2.66990720242

Area: T = 30.02438124642
Perimeter: p = 70.66990720242
Semiperimeter: s = 35.33545360121

Angle ∠ A = α = 137.021988984° = 137°1'12″ = 2.39114482184 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 2.98801101602° = 2°58'48″ = 0.05220127344 rad

Height: ha = 1.71656464265
Height: hb = 1.82196249978
Height: hc = 22.4987566339

Median: ma = 15.55503045866
Median: mb = 18.54221674228
Median: mc = 33.98985129659

Inradius: r = 0.85497016192
Circumradius: R = 25.66994431432

Vertex coordinates: A[2.66990720242; 0] B[0; 0] C[26.81215555092; 22.4987566339]
Centroid: CG[9.82768758445; 7.49991887797]
Coordinates of the circumscribed circle: U[1.33545360121; 25.63547288832]
Coordinates of the inscribed circle: I[2.33545360121; 0.85497016192]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.98801101602° = 42°58'48″ = 2.39114482184 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 177.021988984° = 177°1'12″ = 0.05220127344 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 35 ; ; b = 33 ; ; beta = 40° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 33**2 = 35**2 + c**2 -2 * 33 * c * cos (40° ) ; ; ; ; c**2 -53.623c +136 =0 ; ; p=1; q=-53.6231110183; r=136 ; ; D = q**2 - 4pr = 53.623**2 - 4 * 1 * 136 = 2331.43803528 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 53.62 ± sqrt{ 2331.44 } }{ 2 } ; ; c_{1,2} = 26.8115555092 ± 24.1424834849 ; ; c_{1} = 50.9540389941 ; ;
c_{2} = 2.66907202422 ; ; ; ; (c -50.9540389941) (c -2.66907202422) = 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 = 35 ; ; b = 33 ; ; c = 2.67 ; ;

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

p = a+b+c = 35+33+2.67 = 70.67 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70.67 }{ 2 } = 35.33 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.33 * (35.33-35)(35.33-33)(35.33-2.67) } ; ; T = sqrt{ 901.43 } = 30.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.02 }{ 35 } = 1.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.02 }{ 33 } = 1.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.02 }{ 2.67 } = 22.5 ; ;

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{ 35**2-33**2-2.67**2 }{ 2 * 33 * 2.67 } ) = 137° 1'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 33**2-35**2-2.67**2 }{ 2 * 35 * 2.67 } ) = 40° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.67**2-35**2-33**2 }{ 2 * 33 * 35 } ) = 2° 58'48" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.02 }{ 35.33 } = 0.85 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 35 }{ 2 * sin 137° 1'12" } = 25.67 ; ;




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

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