Triangle calculator SSA

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Triangle has two solutions with side c=93.19771127024 and with side c=70.81876445452

#1 Acute scalene triangle.

Sides: a = 125   b = 95   c = 93.19771127024

Area: T = 4396.047711285
Perimeter: p = 313.1977112702
Semiperimeter: s = 156.5998556351

Angle ∠ A = α = 83.23656175722° = 83°14'8″ = 1.45327355816 rad
Angle ∠ B = β = 49° = 0.85552113335 rad
Angle ∠ C = γ = 47.76443824278° = 47°45'52″ = 0.83436457385 rad

Height: ha = 70.33767538056
Height: hb = 92.54883602705
Height: hc = 94.33986975278

Median: ma = 70.35498465388
Median: mb = 99.49442255009
Median: mc = 100.765494701

Inradius: r = 28.07220794321
Circumradius: R = 62.93881171841

Vertex coordinates: A[93.19771127024; 0] B[0; 0] C[82.00773786238; 94.33986975278]
Centroid: CG[58.40114971087; 31.44662325093]
Coordinates of the circumscribed circle: U[46.59985563512; 42.30658050468]
Coordinates of the inscribed circle: I[61.59985563512; 28.07220794321]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 96.76443824278° = 96°45'52″ = 1.45327355816 rad
∠ B' = β' = 131° = 0.85552113335 rad
∠ C' = γ' = 132.2365617572° = 132°14'8″ = 0.83436457385 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 = 125 ; ; b = 95 ; ; c = 93.2 ; ;

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

p = a+b+c = 125+95+93.2 = 313.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 313.2 }{ 2 } = 156.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 156.6 * (156.6-125)(156.6-95)(156.6-93.2) } ; ; T = sqrt{ 19325230.22 } = 4396.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4396.05 }{ 125 } = 70.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4396.05 }{ 95 } = 92.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4396.05 }{ 93.2 } = 94.34 ; ;

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{ 125**2-95**2-93.2**2 }{ 2 * 95 * 93.2 } ) = 83° 14'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 95**2-125**2-93.2**2 }{ 2 * 125 * 93.2 } ) = 49° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 93.2**2-125**2-95**2 }{ 2 * 95 * 125 } ) = 47° 45'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4396.05 }{ 156.6 } = 28.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 125 }{ 2 * sin 83° 14'8" } = 62.94 ; ;





#2 Obtuse scalene triangle.

Sides: a = 125   b = 95   c = 70.81876445452

Area: T = 3340.422217419
Perimeter: p = 290.8187644545
Semiperimeter: s = 145.4098822273

Angle ∠ A = α = 96.76443824278° = 96°45'52″ = 1.6898857072 rad
Angle ∠ B = β = 49° = 0.85552113335 rad
Angle ∠ C = γ = 34.23656175722° = 34°14'8″ = 0.59875242481 rad

Height: ha = 53.44767547871
Height: hb = 70.32546773514
Height: hc = 94.33986975278

Median: ma = 55.80216074093
Median: mb = 89.79987716479
Median: mc = 105.2219842735

Inradius: r = 22.97326238201
Circumradius: R = 62.93881171841

Vertex coordinates: A[70.81876445452; 0] B[0; 0] C[82.00773786238; 94.33986975278]
Centroid: CG[50.94216743897; 31.44662325093]
Coordinates of the circumscribed circle: U[35.40988222726; 52.0332892481]
Coordinates of the inscribed circle: I[50.40988222726; 22.97326238201]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 83.23656175722° = 83°14'8″ = 1.6898857072 rad
∠ B' = β' = 131° = 0.85552113335 rad
∠ C' = γ' = 145.7644382428° = 145°45'52″ = 0.59875242481 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 125 ; ; b = 95 ; ; beta = 49° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 95**2 = 125**2 + c**2 -2 * 95 * c * cos (49° ) ; ; ; ; c**2 -164.015c +6600 =0 ; ; p=1; q=-164.014757248; r=6600 ; ; D = q**2 - 4pr = 164.015**2 - 4 * 1 * 6600 = 500.840594998 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 164.01 ± sqrt{ 500.84 } }{ 2 } ; ; c_{1,2} = 82.0073786238 ± 11.1897340786 ; ; c_{1} = 93.1971127024 ; ;
c_{2} = 70.8176445452 ; ; ; ; (c -93.1971127024) (c -70.8176445452) = 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 = 125 ; ; b = 95 ; ; c = 70.82 ; ;

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

p = a+b+c = 125+95+70.82 = 290.82 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 290.82 }{ 2 } = 145.41 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 145.41 * (145.41-125)(145.41-95)(145.41-70.82) } ; ; T = sqrt{ 11158420.3 } = 3340.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3340.42 }{ 125 } = 53.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3340.42 }{ 95 } = 70.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3340.42 }{ 70.82 } = 94.34 ; ;

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{ 125**2-95**2-70.82**2 }{ 2 * 95 * 70.82 } ) = 96° 45'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 95**2-125**2-70.82**2 }{ 2 * 125 * 70.82 } ) = 49° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 70.82**2-125**2-95**2 }{ 2 * 95 * 125 } ) = 34° 14'8" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3340.42 }{ 145.41 } = 22.97 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 125 }{ 2 * sin 96° 45'52" } = 62.94 ; ;




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