Triangle calculator SSA

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Triangle has two solutions with side c=60.30884679844 and with side c=15.12222544774

#1 Obtuse scalene triangle.

Sides: a = 44   b = 32   c = 60.30884679844

Area: T = 683.3455459532
Perimeter: p = 136.3088467984
Semiperimeter: s = 68.15442339922

Angle ∠ A = α = 45.08768125955° = 45°5'13″ = 0.7876913329 rad
Angle ∠ B = β = 31° = 0.54110520681 rad
Angle ∠ C = γ = 103.9133187405° = 103°54'47″ = 1.81436272565 rad

Height: ha = 31.06111572515
Height: hb = 42.70990912208
Height: hc = 22.6621675296

Median: ma = 42.97215679876
Median: mb = 50.30546285675
Median: mc = 23.89897922206

Inradius: r = 10.02664564577
Circumradius: R = 31.06656644226

Vertex coordinates: A[60.30884679844; 0] B[0; 0] C[37.71553612309; 22.6621675296]
Centroid: CG[32.67546097384; 7.55438917653]
Coordinates of the circumscribed circle: U[30.15442339922; -7.47697843582]
Coordinates of the inscribed circle: I[36.15442339922; 10.02664564577]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9133187405° = 134°54'47″ = 0.7876913329 rad
∠ B' = β' = 149° = 0.54110520681 rad
∠ C' = γ' = 76.08768125955° = 76°5'13″ = 1.81436272565 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 = 44 ; ; b = 32 ; ; c = 60.31 ; ;

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

p = a+b+c = 44+32+60.31 = 136.31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 136.31 }{ 2 } = 68.15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 68.15 * (68.15-44)(68.15-32)(68.15-60.31) } ; ; T = sqrt{ 466961.02 } = 683.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 683.35 }{ 44 } = 31.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 683.35 }{ 32 } = 42.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 683.35 }{ 60.31 } = 22.66 ; ;

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{ 44**2-32**2-60.31**2 }{ 2 * 32 * 60.31 } ) = 45° 5'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 32**2-44**2-60.31**2 }{ 2 * 44 * 60.31 } ) = 31° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 60.31**2-44**2-32**2 }{ 2 * 32 * 44 } ) = 103° 54'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 683.35 }{ 68.15 } = 10.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 44 }{ 2 * sin 45° 5'13" } = 31.07 ; ;





#2 Obtuse scalene triangle.

Sides: a = 44   b = 32   c = 15.12222544774

Area: T = 171.3487810355
Perimeter: p = 91.12222544774
Semiperimeter: s = 45.56111272387

Angle ∠ A = α = 134.9133187405° = 134°54'47″ = 2.35546793246 rad
Angle ∠ B = β = 31° = 0.54110520681 rad
Angle ∠ C = γ = 14.08768125955° = 14°5'13″ = 0.24658612609 rad

Height: ha = 7.78985368343
Height: hb = 10.70992381472
Height: hc = 22.6621675296

Median: ma = 11.9310686914
Median: mb = 28.74661526163
Median: mc = 37.72204103223

Inradius: r = 3.76108334284
Circumradius: R = 31.06656644226

Vertex coordinates: A[15.12222544774; 0] B[0; 0] C[37.71553612309; 22.6621675296]
Centroid: CG[17.61325385694; 7.55438917653]
Coordinates of the circumscribed circle: U[7.56111272387; 30.13114596543]
Coordinates of the inscribed circle: I[13.56111272387; 3.76108334284]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 45.08768125955° = 45°5'13″ = 2.35546793246 rad
∠ B' = β' = 149° = 0.54110520681 rad
∠ C' = γ' = 165.9133187405° = 165°54'47″ = 0.24658612609 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 44 ; ; b = 32 ; ; beta = 31° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 32**2 = 44**2 + c**2 -2 * 32 * c * cos (31° ) ; ; ; ; c**2 -75.431c +912 =0 ; ; p=1; q=-75.4307224618; r=912 ; ; D = q**2 - 4pr = 75.431**2 - 4 * 1 * 912 = 2041.79389111 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 75.43 ± sqrt{ 2041.79 } }{ 2 } ; ; c_{1,2} = 37.7153612309 ± 22.5931067535 ; ; c_{1} = 60.3084679844 ; ;
c_{2} = 15.1222544774 ; ; ; ; (c -60.3084679844) (c -15.1222544774) = 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 = 44 ; ; b = 32 ; ; c = 15.12 ; ;

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

p = a+b+c = 44+32+15.12 = 91.12 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 91.12 }{ 2 } = 45.56 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45.56 * (45.56-44)(45.56-32)(45.56-15.12) } ; ; T = sqrt{ 29360.07 } = 171.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.35 }{ 44 } = 7.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.35 }{ 32 } = 10.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.35 }{ 15.12 } = 22.66 ; ;

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{ 44**2-32**2-15.12**2 }{ 2 * 32 * 15.12 } ) = 134° 54'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 32**2-44**2-15.12**2 }{ 2 * 44 * 15.12 } ) = 31° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15.12**2-44**2-32**2 }{ 2 * 32 * 44 } ) = 14° 5'13" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.35 }{ 45.56 } = 3.76 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 44 }{ 2 * sin 134° 54'47" } = 31.07 ; ;




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