Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=126.3888321747 and with side c=15.03330344904

#1 Acute scalene triangle.

Sides: a = 100   b = 90   c = 126.3888321747

Area: T = 4468.50219685
Perimeter: p = 316.3888321747
Semiperimeter: s = 158.1944160874

Angle ∠ A = α = 51.78330767038° = 51°46'59″ = 0.90437851853 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 83.21769232962° = 83°13'1″ = 1.45224093049 rad

Height: ha = 89.37700393701
Height: hb = 99.33000437445
Height: hc = 70.71106781187

Median: ma = 97.65875851483
Median: mb = 104.7699589001
Median: mc = 71.10990573099

Inradius: r = 28.24769463084
Circumradius: R = 63.64396103068

Vertex coordinates: A[126.3888321747; 0] B[0; 0] C[70.71106781187; 70.71106781187]
Centroid: CG[65.76996666219; 23.57702260396]
Coordinates of the circumscribed circle: U[63.19441608735; 7.51765172452]
Coordinates of the inscribed circle: I[68.19441608735; 28.24769463084]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.2176923296° = 128°13'1″ = 0.90437851853 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 96.78330767038° = 96°46'59″ = 1.45224093049 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 = 100 ; ; b = 90 ; ; c = 126.39 ; ;

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

p = a+b+c = 100+90+126.39 = 316.39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 316.39 }{ 2 } = 158.19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 158.19 * (158.19-100)(158.19-90)(158.19-126.39) } ; ; T = sqrt{ 19967509.84 } = 4468.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4468.5 }{ 100 } = 89.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4468.5 }{ 90 } = 99.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4468.5 }{ 126.39 } = 70.71 ; ;

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{ 100**2-90**2-126.39**2 }{ 2 * 90 * 126.39 } ) = 51° 46'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 90**2-100**2-126.39**2 }{ 2 * 100 * 126.39 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 126.39**2-100**2-90**2 }{ 2 * 90 * 100 } ) = 83° 13'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4468.5 }{ 158.19 } = 28.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 51° 46'59" } = 63.64 ; ;





#2 Obtuse scalene triangle.

Sides: a = 100   b = 90   c = 15.03330344904

Area: T = 531.4988031497
Perimeter: p = 205.033303449
Semiperimeter: s = 102.5176517245

Angle ∠ A = α = 128.2176923296° = 128°13'1″ = 2.23878074683 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 6.78330767038° = 6°46'59″ = 0.11883870219 rad

Height: ha = 10.63299606299
Height: hb = 11.81110673666
Height: hc = 70.71106781187

Median: ma = 40.78798487368
Median: mb = 55.57697405338
Median: mc = 94.8344075988

Inradius: r = 5.18545111966
Circumradius: R = 63.64396103068

Vertex coordinates: A[15.03330344904; 0] B[0; 0] C[70.71106781187; 70.71106781187]
Centroid: CG[28.58112375363; 23.57702260396]
Coordinates of the circumscribed circle: U[7.51765172452; 63.19441608735]
Coordinates of the inscribed circle: I[12.51765172452; 5.18545111966]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 51.78330767038° = 51°46'59″ = 2.23878074683 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 173.2176923296° = 173°13'1″ = 0.11883870219 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 100 ; ; b = 90 ; ; beta = 45° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 90**2 = 100**2 + c**2 -2 * 90 * c * cos (45° ) ; ; ; ; c**2 -141.421c +1900 =0 ; ; p=1; q=-141.421356237; r=1900 ; ; D = q**2 - 4pr = 141.421**2 - 4 * 1 * 1900 = 12400 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 141.42 ± sqrt{ 12400 } }{ 2 } = fraction{ 141.42 ± 20 sqrt{ 31 } }{ 2 } ; ; c_{1,2} = 70.7106781187 ± 55.6776436283 ; ;
c_{1} = 126.388321747 ; ; c_{2} = 15.0330344904 ; ; ; ; (c -126.388321747) (c -15.0330344904) = 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 = 100 ; ; b = 90 ; ; c = 15.03 ; ;

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

p = a+b+c = 100+90+15.03 = 205.03 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 205.03 }{ 2 } = 102.52 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 102.52 * (102.52-100)(102.52-90)(102.52-15.03) } ; ; T = sqrt{ 282490.16 } = 531.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 531.5 }{ 100 } = 10.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 531.5 }{ 90 } = 11.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 531.5 }{ 15.03 } = 70.71 ; ;

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{ 100**2-90**2-15.03**2 }{ 2 * 90 * 15.03 } ) = 128° 13'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 90**2-100**2-15.03**2 }{ 2 * 100 * 15.03 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15.03**2-100**2-90**2 }{ 2 * 90 * 100 } ) = 6° 46'59" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 531.5 }{ 102.52 } = 5.18 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 128° 13'1" } = 63.64 ; ;




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

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