Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=42.39993927704 and with side c=9.3166171157

#1 Acute scalene triangle.

Sides: a = 42   b = 37   c = 42.39993927704

Area: T = 701.6354726439
Perimeter: p = 121.399939277
Semiperimeter: s = 60.76996963852

Angle ∠ A = α = 63.44441109646° = 63°26'39″ = 1.10773086273 rad
Angle ∠ B = β = 52° = 0.9087571211 rad
Angle ∠ C = γ = 64.55658890354° = 64°33'21″ = 1.12767128152 rad

Height: ha = 33.41111774495
Height: hb = 37.92662014291
Height: hc = 33.09664516515

Median: ma = 33.79987315391
Median: mb = 37.92989368906
Median: mc = 33.42326401287

Inradius: r = 11.55991142662
Circumradius: R = 23.47768369788

Vertex coordinates: A[42.39993927704; 0] B[0; 0] C[25.85877819637; 33.09664516515]
Centroid: CG[22.7522391578; 11.03221505505]
Coordinates of the circumscribed circle: U[21.21996963852; 10.08663644445]
Coordinates of the inscribed circle: I[23.76996963852; 11.55991142662]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5565889035° = 116°33'21″ = 1.10773086273 rad
∠ B' = β' = 128° = 0.9087571211 rad
∠ C' = γ' = 115.4444110965° = 115°26'39″ = 1.12767128152 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 = 42 ; ; b = 37 ; ; c = 42.4 ; ;

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

p = a+b+c = 42+37+42.4 = 121.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 121.4 }{ 2 } = 60.7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60.7 * (60.7-42)(60.7-37)(60.7-42.4) } ; ; T = sqrt{ 492291.29 } = 701.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 701.63 }{ 42 } = 33.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 701.63 }{ 37 } = 37.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 701.63 }{ 42.4 } = 33.1 ; ;

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{ 42**2-37**2-42.4**2 }{ 2 * 37 * 42.4 } ) = 63° 26'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 37**2-42**2-42.4**2 }{ 2 * 42 * 42.4 } ) = 52° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42.4**2-42**2-37**2 }{ 2 * 37 * 42 } ) = 64° 33'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 701.63 }{ 60.7 } = 11.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 42 }{ 2 * sin 63° 26'39" } = 23.48 ; ;





#2 Obtuse scalene triangle.

Sides: a = 42   b = 37   c = 9.3166171157

Area: T = 154.1666104136
Perimeter: p = 88.3166171157
Semiperimeter: s = 44.15880855785

Angle ∠ A = α = 116.5565889035° = 116°33'21″ = 2.03442840263 rad
Angle ∠ B = β = 52° = 0.9087571211 rad
Angle ∠ C = γ = 11.44441109646° = 11°26'39″ = 0.21997374163 rad

Height: ha = 7.34112430541
Height: hb = 8.33333029263
Height: hc = 33.09664516515

Median: ma = 16.93879905099
Median: mb = 24.14884062106
Median: mc = 39.30439723023

Inradius: r = 3.49112316084
Circumradius: R = 23.47768369788

Vertex coordinates: A[9.3166171157; 0] B[0; 0] C[25.85877819637; 33.09664516515]
Centroid: CG[11.72546510402; 11.03221505505]
Coordinates of the circumscribed circle: U[4.65880855785; 23.0110087207]
Coordinates of the inscribed circle: I[7.15880855785; 3.49112316084]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 63.44441109646° = 63°26'39″ = 2.03442840263 rad
∠ B' = β' = 128° = 0.9087571211 rad
∠ C' = γ' = 168.5565889035° = 168°33'21″ = 0.21997374163 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 42 ; ; b = 37 ; ; beta = 52° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 37**2 = 42**2 + c**2 -2 * 37 * c * cos (52° ) ; ; ; ; c**2 -51.716c +395 =0 ; ; p=1; q=-51.7155639274; r=395 ; ; D = q**2 - 4pr = 51.716**2 - 4 * 1 * 395 = 1094.49955232 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 51.72 ± sqrt{ 1094.5 } }{ 2 } ; ; c_{1,2} = 25.8577819637 ± 16.5416108067 ; ; c_{1} = 42.3993927704 ; ;
c_{2} = 9.31617115695 ; ; ; ; (c -42.3993927704) (c -9.31617115695) = 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 = 42 ; ; b = 37 ; ; c = 9.32 ; ;

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

p = a+b+c = 42+37+9.32 = 88.32 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 88.32 }{ 2 } = 44.16 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 44.16 * (44.16-42)(44.16-37)(44.16-9.32) } ; ; T = sqrt{ 23767.19 } = 154.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 154.17 }{ 42 } = 7.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 154.17 }{ 37 } = 8.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 154.17 }{ 9.32 } = 33.1 ; ;

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{ 42**2-37**2-9.32**2 }{ 2 * 37 * 9.32 } ) = 116° 33'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 37**2-42**2-9.32**2 }{ 2 * 42 * 9.32 } ) = 52° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.32**2-42**2-37**2 }{ 2 * 37 * 42 } ) = 11° 26'39" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 154.17 }{ 44.16 } = 3.49 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 42 }{ 2 * sin 116° 33'21" } = 23.48 ; ;




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

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