Triangle calculator SSA

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Triangle has two solutions with side c=9.06771430981 and with side c=1.49222010002

#1 Obtuse scalene triangle.

Sides: a = 6.7   b = 5.6   c = 9.06771430981

Area: T = 18.70106738342
Perimeter: p = 21.36771430981
Semiperimeter: s = 10.68435715491

Angle ∠ A = α = 47.44221621532° = 47°26'32″ = 0.82880219338 rad
Angle ∠ B = β = 38° = 0.66332251158 rad
Angle ∠ C = γ = 94.55878378468° = 94°33'28″ = 1.6550345604 rad

Height: ha = 5.58222906968
Height: hb = 6.67988120837
Height: hc = 4.12549318847

Median: ma = 6.75501142198
Median: mb = 7.46440164778
Median: mc = 4.1921864622

Inradius: r = 1.75504140585
Circumradius: R = 4.54879538874

Vertex coordinates: A[9.06771430981; 0] B[0; 0] C[5.28796720492; 4.12549318847]
Centroid: CG[4.78222717158; 1.37549772949]
Coordinates of the circumscribed circle: U[4.53435715491; -0.36114049958]
Coordinates of the inscribed circle: I[5.08435715491; 1.75504140585]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.5587837847° = 132°33'28″ = 0.82880219338 rad
∠ B' = β' = 142° = 0.66332251158 rad
∠ C' = γ' = 85.44221621532° = 85°26'32″ = 1.6550345604 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 = 6.7 ; ; b = 5.6 ; ; c = 9.07 ; ;

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

p = a+b+c = 6.7+5.6+9.07 = 21.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.37 }{ 2 } = 10.68 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.68 * (10.68-6.7)(10.68-5.6)(10.68-9.07) } ; ; T = sqrt{ 349.72 } = 18.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.7 }{ 6.7 } = 5.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.7 }{ 5.6 } = 6.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.7 }{ 9.07 } = 4.12 ; ;

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{ 6.7**2-5.6**2-9.07**2 }{ 2 * 5.6 * 9.07 } ) = 47° 26'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.6**2-6.7**2-9.07**2 }{ 2 * 6.7 * 9.07 } ) = 38° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.07**2-6.7**2-5.6**2 }{ 2 * 5.6 * 6.7 } ) = 94° 33'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.7 }{ 10.68 } = 1.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.7 }{ 2 * sin 47° 26'32" } = 4.55 ; ;





#2 Obtuse scalene triangle.

Sides: a = 6.7   b = 5.6   c = 1.49222010002

Area: T = 3.0787613742
Perimeter: p = 13.79222010002
Semiperimeter: s = 6.89661005001

Angle ∠ A = α = 132.5587837847° = 132°33'28″ = 2.31435707198 rad
Angle ∠ B = β = 38° = 0.66332251158 rad
Angle ∠ C = γ = 9.44221621532° = 9°26'32″ = 0.16547968181 rad

Height: ha = 0.91986906693
Height: hb = 1.0999147765
Height: hc = 4.12549318847

Median: ma = 2.3660260984
Median: mb = 3.9654635155
Median: mc = 6.12993012688

Inradius: r = 0.44662831918
Circumradius: R = 4.54879538874

Vertex coordinates: A[1.49222010002; 0] B[0; 0] C[5.28796720492; 4.12549318847]
Centroid: CG[2.25772910165; 1.37549772949]
Coordinates of the circumscribed circle: U[0.74661005001; 4.48663368805]
Coordinates of the inscribed circle: I[1.29661005001; 0.44662831918]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 47.44221621532° = 47°26'32″ = 2.31435707198 rad
∠ B' = β' = 142° = 0.66332251158 rad
∠ C' = γ' = 170.5587837847° = 170°33'28″ = 0.16547968181 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 6.7 ; ; b = 5.6 ; ; beta = 38° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 5.6**2 = 6.7**2 + c**2 -2 * 5.6 * c * cos (38° ) ; ; ; ; c**2 -10.559c +13.53 =0 ; ; p=1; q=-10.5593440983; r=13.53 ; ; D = q**2 - 4pr = 10.559**2 - 4 * 1 * 13.53 = 57.3797477869 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 10.56 ± sqrt{ 57.38 } }{ 2 } ; ; c_{1,2} = 5.27967204917 ± 3.78747104896 ; ; c_{1} = 9.06714309813 ; ;
c_{2} = 1.4922010002 ; ; ; ; (c -9.06714309813) (c -1.4922010002) = 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 = 6.7 ; ; b = 5.6 ; ; c = 1.49 ; ;

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

p = a+b+c = 6.7+5.6+1.49 = 13.79 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.79 }{ 2 } = 6.9 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.9 * (6.9-6.7)(6.9-5.6)(6.9-1.49) } ; ; T = sqrt{ 9.47 } = 3.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.08 }{ 6.7 } = 0.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.08 }{ 5.6 } = 1.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.08 }{ 1.49 } = 4.12 ; ;

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{ 6.7**2-5.6**2-1.49**2 }{ 2 * 5.6 * 1.49 } ) = 132° 33'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.6**2-6.7**2-1.49**2 }{ 2 * 6.7 * 1.49 } ) = 38° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.49**2-6.7**2-5.6**2 }{ 2 * 5.6 * 6.7 } ) = 9° 26'32" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.08 }{ 6.9 } = 0.45 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.7 }{ 2 * sin 132° 33'28" } = 4.55 ; ;




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