Triangle calculator SSA

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Triangle has two solutions with side c=25.4111158487 and with side c=9.30442157098

#1 Obtuse scalene triangle.

Sides: a = 17.97   b = 9.3   c = 25.4111158487

Area: T = 59.09333725943
Perimeter: p = 52.6811158487
Semiperimeter: s = 26.34105792435

Angle ∠ A = α = 30.00769593698° = 30°25″ = 0.52437202395 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 134.993304063° = 134°59'35″ = 2.35660730263 rad

Height: ha = 6.57768917745
Height: hb = 12.70882521708
Height: hc = 4.65109782405

Median: ma = 16.89331424793
Median: mb = 21.51104959921
Median: mc = 6.57882753125

Inradius: r = 2.24334348177
Circumradius: R = 17.9666220369

Vertex coordinates: A[25.4111158487; 0] B[0; 0] C[17.35876870984; 4.65109782405]
Centroid: CG[14.25662818618; 1.55503260802]
Coordinates of the circumscribed circle: U[12.70655792435; -12.70224930795]
Coordinates of the inscribed circle: I[17.04105792435; 2.24334348177]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.993304063° = 149°59'35″ = 0.52437202395 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 45.00769593698° = 45°25″ = 2.35660730263 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 = 17.97 ; ; b = 9.3 ; ; c = 25.41 ; ;

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

p = a+b+c = 17.97+9.3+25.41 = 52.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52.68 }{ 2 } = 26.34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.34 * (26.34-17.97)(26.34-9.3)(26.34-25.41) } ; ; T = sqrt{ 3492.03 } = 59.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.09 }{ 17.97 } = 6.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.09 }{ 9.3 } = 12.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.09 }{ 25.41 } = 4.65 ; ;

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{ 17.97**2-9.3**2-25.41**2 }{ 2 * 9.3 * 25.41 } ) = 30° 25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.3**2-17.97**2-25.41**2 }{ 2 * 17.97 * 25.41 } ) = 15° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25.41**2-17.97**2-9.3**2 }{ 2 * 9.3 * 17.97 } ) = 134° 59'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.09 }{ 26.34 } = 2.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.97 }{ 2 * sin 30° 25" } = 17.97 ; ;





#2 Obtuse scalene triangle.

Sides: a = 17.97   b = 9.3   c = 9.30442157098

Area: T = 21.63768524057
Perimeter: p = 36.57442157098
Semiperimeter: s = 18.28771078549

Angle ∠ A = α = 149.993304063° = 149°59'35″ = 2.61878724141 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 15.00769593698° = 15°25″ = 0.26219208517 rad

Height: ha = 2.40881082255
Height: hb = 4.65330865389
Height: hc = 4.65109782405

Median: ma = 2.40881092142
Median: mb = 13.5322263853
Median: mc = 13.53300902623

Inradius: r = 1.18331751952
Circumradius: R = 17.9666220369

Vertex coordinates: A[9.30442157098; 0] B[0; 0] C[17.35876870984; 4.65109782405]
Centroid: CG[8.88773009361; 1.55503260802]
Coordinates of the circumscribed circle: U[4.65221078549; 17.353347132]
Coordinates of the inscribed circle: I[8.98771078549; 1.18331751952]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.00769593698° = 30°25″ = 2.61878724141 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 164.993304063° = 164°59'35″ = 0.26219208517 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 17.97 ; ; b = 9.3 ; ; beta = 15° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 9.3**2 = 17.97**2 + c**2 -2 * 9.3 * c * cos (15° ) ; ; ; ; c**2 -34.715c +236.431 =0 ; ; p=1; q=-34.7153741968; r=236.4309 ; ; D = q**2 - 4pr = 34.715**2 - 4 * 1 * 236.431 = 259.433605626 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 34.72 ± sqrt{ 259.43 } }{ 2 } ; ; c_{1,2} = 17.3576870984 ± 8.05347138857 ; ;
c_{1} = 25.411158487 ; ; c_{2} = 9.30421570985 ; ; ; ; (c -25.411158487) (c -9.30421570985) = 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 = 17.97 ; ; b = 9.3 ; ; c = 9.3 ; ;

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

p = a+b+c = 17.97+9.3+9.3 = 36.57 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36.57 }{ 2 } = 18.29 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.29 * (18.29-17.97)(18.29-9.3)(18.29-9.3) } ; ; T = sqrt{ 468.15 } = 21.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.64 }{ 17.97 } = 2.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.64 }{ 9.3 } = 4.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.64 }{ 9.3 } = 4.65 ; ;

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{ 17.97**2-9.3**2-9.3**2 }{ 2 * 9.3 * 9.3 } ) = 149° 59'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.3**2-17.97**2-9.3**2 }{ 2 * 17.97 * 9.3 } ) = 15° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.3**2-17.97**2-9.3**2 }{ 2 * 9.3 * 17.97 } ) = 15° 25" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.64 }{ 18.29 } = 1.18 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.97 }{ 2 * sin 149° 59'35" } = 17.97 ; ;




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