Triangle calculator SSA

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Triangle has two solutions with side c=14.56223604111 and with side c=0.81331992112

#1 Obtuse scalene triangle.

Sides: a = 7.89   b = 7.1   c = 14.56223604111

Area: T = 12.92331033048
Perimeter: p = 29.55223604111
Semiperimeter: s = 14.77661802055

Angle ∠ A = α = 14.47663771888° = 14°28'35″ = 0.25326604457 rad
Angle ∠ B = β = 13° = 0.22768928028 rad
Angle ∠ C = γ = 152.5243622811° = 152°31'25″ = 2.66220394051 rad

Height: ha = 3.27658183282
Height: hb = 3.64403107901
Height: hc = 1.77548638188

Median: ma = 10.75551450651
Median: mb = 11.16604086113
Median: mc = 1.82108417873

Inradius: r = 0.87545902612
Circumradius: R = 15.78112107632

Vertex coordinates: A[14.56223604111; 0] B[0; 0] C[7.68877798112; 1.77548638188]
Centroid: CG[7.41767134074; 0.59216212729]
Coordinates of the circumscribed circle: U[7.28111802055; -14.00111080978]
Coordinates of the inscribed circle: I[7.67661802055; 0.87545902612]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.5243622811° = 165°31'25″ = 0.25326604457 rad
∠ B' = β' = 167° = 0.22768928028 rad
∠ C' = γ' = 27.47663771888° = 27°28'35″ = 2.66220394051 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 = 7.89 ; ; b = 7.1 ; ; c = 14.56 ; ;

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

p = a+b+c = 7.89+7.1+14.56 = 29.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.55 }{ 2 } = 14.78 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.78 * (14.78-7.89)(14.78-7.1)(14.78-14.56) } ; ; T = sqrt{ 167.01 } = 12.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.92 }{ 7.89 } = 3.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.92 }{ 7.1 } = 3.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.92 }{ 14.56 } = 1.77 ; ;

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{ 7.89**2-7.1**2-14.56**2 }{ 2 * 7.1 * 14.56 } ) = 14° 28'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.1**2-7.89**2-14.56**2 }{ 2 * 7.89 * 14.56 } ) = 13° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14.56**2-7.89**2-7.1**2 }{ 2 * 7.1 * 7.89 } ) = 152° 31'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.92 }{ 14.78 } = 0.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.89 }{ 2 * sin 14° 28'35" } = 15.78 ; ;





#2 Obtuse scalene triangle.

Sides: a = 7.89   b = 7.1   c = 0.81331992112

Area: T = 0.72216589287
Perimeter: p = 15.80331992112
Semiperimeter: s = 7.90215996056

Angle ∠ A = α = 165.5243622811° = 165°31'25″ = 2.88989322079 rad
Angle ∠ B = β = 13° = 0.22768928028 rad
Angle ∠ C = γ = 1.47663771888° = 1°28'35″ = 0.02657676429 rad

Height: ha = 0.183293002
Height: hb = 0.20332842053
Height: hc = 1.77548638188

Median: ma = 3.15879457688
Median: mb = 4.34221419229
Median: mc = 7.49443796782

Inradius: r = 0.09113307387
Circumradius: R = 15.78112107632

Vertex coordinates: A[0.81331992112; 0] B[0; 0] C[7.68877798112; 1.77548638188]
Centroid: CG[2.83436596741; 0.59216212729]
Coordinates of the circumscribed circle: U[0.40765996056; 15.77659719166]
Coordinates of the inscribed circle: I[0.80215996056; 0.09113307387]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 14.47663771888° = 14°28'35″ = 2.88989322079 rad
∠ B' = β' = 167° = 0.22768928028 rad
∠ C' = γ' = 178.5243622811° = 178°31'25″ = 0.02657676429 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 7.89 ; ; b = 7.1 ; ; beta = 13° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 7.1**2 = 7.89**2 + c**2 -2 * 7.1 * c * cos (13° ) ; ; ; ; c**2 -15.376c +11.842 =0 ; ; p=1; q=-15.3755596223; r=11.8421 ; ; D = q**2 - 4pr = 15.376**2 - 4 * 1 * 11.842 = 189.039433699 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 15.38 ± sqrt{ 189.04 } }{ 2 } ; ; c_{1,2} = 7.68777981116 ± 6.87458059992 ; ;
c_{1} = 14.5623604111 ; ; c_{2} = 0.813199211235 ; ; ; ; (c -14.5623604111) (c -0.813199211235) = 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 = 7.89 ; ; b = 7.1 ; ; c = 0.81 ; ;

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

p = a+b+c = 7.89+7.1+0.81 = 15.8 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.8 }{ 2 } = 7.9 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.9 * (7.9-7.89)(7.9-7.1)(7.9-0.81) } ; ; T = sqrt{ 0.52 } = 0.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.72 }{ 7.89 } = 0.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.72 }{ 7.1 } = 0.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.72 }{ 0.81 } = 1.77 ; ;

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{ 7.89**2-7.1**2-0.81**2 }{ 2 * 7.1 * 0.81 } ) = 165° 31'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.1**2-7.89**2-0.81**2 }{ 2 * 7.89 * 0.81 } ) = 13° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.81**2-7.89**2-7.1**2 }{ 2 * 7.1 * 7.89 } ) = 1° 28'35" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.72 }{ 7.9 } = 0.09 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.89 }{ 2 * sin 165° 31'25" } = 15.78 ; ;




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