Triangle calculator SSA

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Triangle has two solutions with side c=5.84662287756 and with side c=1.14879553725

#1 Obtuse scalene triangle.

Sides: a = 3.531146   b = 2.4   c = 5.84662287756

Area: T = 1.43766646507
Perimeter: p = 11.77876887756
Semiperimeter: s = 5.88988443878

Angle ∠ A = α = 11.81769192781° = 11°49'1″ = 0.20662441488 rad
Angle ∠ B = β = 8° = 0.14396263402 rad
Angle ∠ C = γ = 160.1833080722° = 160°10'59″ = 2.79657221646 rad

Height: ha = 0.81436377876
Height: hb = 1.19772205423
Height: hc = 0.49114842391

Median: ma = 4.1055044825
Median: mb = 4.67881193138
Median: mc = 0.7565650145

Inradius: r = 0.24439637654
Circumradius: R = 8.62223558412

Vertex coordinates: A[5.84662287756; 0] B[0; 0] C[3.4977092074; 0.49114842391]
Centroid: CG[3.11444402832; 0.16438280797]
Coordinates of the circumscribed circle: U[2.92331143878; -8.11217459605]
Coordinates of the inscribed circle: I[3.48988443878; 0.24439637654]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.1833080722° = 168°10'59″ = 0.20662441488 rad
∠ B' = β' = 172° = 0.14396263402 rad
∠ C' = γ' = 19.81769192781° = 19°49'1″ = 2.79657221646 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 = 3.53 ; ; b = 2.4 ; ; c = 5.85 ; ;

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

p = a+b+c = 3.53+2.4+5.85 = 11.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.78 }{ 2 } = 5.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.89 * (5.89-3.53)(5.89-2.4)(5.89-5.85) } ; ; T = sqrt{ 2.06 } = 1.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.44 }{ 3.53 } = 0.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.44 }{ 2.4 } = 1.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.44 }{ 5.85 } = 0.49 ; ;

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{ 3.53**2-2.4**2-5.85**2 }{ 2 * 2.4 * 5.85 } ) = 11° 49'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.4**2-3.53**2-5.85**2 }{ 2 * 3.53 * 5.85 } ) = 8° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.85**2-3.53**2-2.4**2 }{ 2 * 2.4 * 3.53 } ) = 160° 10'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.44 }{ 5.89 } = 0.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.53 }{ 2 * sin 11° 49'1" } = 8.62 ; ;





#2 Obtuse scalene triangle.

Sides: a = 3.531146   b = 2.4   c = 1.14879553725

Area: T = 0.28221009864
Perimeter: p = 7.07994153725
Semiperimeter: s = 3.54397076862

Angle ∠ A = α = 168.1833080722° = 168°10'59″ = 2.93553485047 rad
Angle ∠ B = β = 8° = 0.14396263402 rad
Angle ∠ C = γ = 3.81769192781° = 3°49'1″ = 0.06766178087 rad

Height: ha = 0.16597645089
Height: hb = 0.23550841553
Height: hc = 0.49114842391

Median: ma = 0.64989209009
Median: mb = 2.33554883075
Median: mc = 2.96441448145

Inradius: r = 0.0879696125
Circumradius: R = 8.62223558412

Vertex coordinates: A[1.14879553725; 0] B[0; 0] C[3.4977092074; 0.49114842391]
Centroid: CG[1.54883491488; 0.16438280797]
Coordinates of the circumscribed circle: U[0.57439776862; 8.60332301996]
Coordinates of the inscribed circle: I[1.14397076862; 0.0879696125]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 11.81769192781° = 11°49'1″ = 2.93553485047 rad
∠ B' = β' = 172° = 0.14396263402 rad
∠ C' = γ' = 176.1833080722° = 176°10'59″ = 0.06766178087 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 3.53 ; ; b = 2.4 ; ; beta = 8° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 2.4**2 = 3.53**2 + c**2 -2 * 2.4 * c * cos (8° ) ; ; ; ; c**2 -6.994c +6.711 =0 ; ; p=1; q=-6.99418414808; r=6.7112097316 ; ; D = q**2 - 4pr = 6.994**2 - 4 * 1 * 6.711 = 22.0737729708 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 6.99 ± sqrt{ 22.07 } }{ 2 } ; ; c_{1,2} = 3.49709207404 ± 2.34913670158 ; ;
c_{1} = 5.84622877562 ; ; c_{2} = 1.14795537246 ; ; ; ; (c -5.84622877562) (c -1.14795537246) = 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 = 3.53 ; ; b = 2.4 ; ; c = 1.15 ; ;

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

p = a+b+c = 3.53+2.4+1.15 = 7.08 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.08 }{ 2 } = 3.54 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.54 * (3.54-3.53)(3.54-2.4)(3.54-1.15) } ; ; T = sqrt{ 0.08 } = 0.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.28 }{ 3.53 } = 0.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.28 }{ 2.4 } = 0.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.28 }{ 1.15 } = 0.49 ; ;

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{ 3.53**2-2.4**2-1.15**2 }{ 2 * 2.4 * 1.15 } ) = 168° 10'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.4**2-3.53**2-1.15**2 }{ 2 * 3.53 * 1.15 } ) = 8° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.15**2-3.53**2-2.4**2 }{ 2 * 2.4 * 3.53 } ) = 3° 49'1" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.28 }{ 3.54 } = 0.08 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.53 }{ 2 * sin 168° 10'59" } = 8.62 ; ;




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