Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, c and angle α.

Triangle has two solutions: a=59; b=4.35664463888; c=62 and a=59; b=83.32547944784; c=62.

#1 Obtuse scalene triangle.

Sides: a = 59   b = 4.35664463888   c = 62

Area: T = 95.49546562845
Perimeter: p = 125.3566446389
Semiperimeter: s = 62.67882231944

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 2.99328538608° = 2°59'34″ = 0.05222351539 rad
Angle ∠ C = γ = 132.0077146139° = 132°26″ = 2.30439593363 rad

Height: ha = 3.23771069927
Height: hb = 43.84106204336
Height: hc = 3.08804727834

Median: ma = 32.57766682239
Median: mb = 60.47993794918
Median: mc = 28.08989535684

Inradius: r = 1.52435699325
Circumradius: R = 41.719930009

Vertex coordinates: A[62; 0] B[0; 0] C[58.92195272166; 3.08804727834]
Centroid: CG[40.30765090722; 1.02768242611]
Coordinates of the circumscribed circle: U[31; -27.92195272166]
Coordinates of the inscribed circle: I[58.32217768056; 1.52435699325]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 177.0077146139° = 177°26″ = 0.05222351539 rad
∠ C' = γ' = 47.99328538608° = 47°59'34″ = 2.30439593363 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 = 59 ; ; b = 4.36 ; ; c = 62 ; ;

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

p = a+b+c = 59+4.36+62 = 125.36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 125.36 }{ 2 } = 62.68 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 62.68 * (62.68-59)(62.68-4.36)(62.68-62) } ; ; T = sqrt{ 9119.23 } = 95.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.49 }{ 59 } = 3.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.49 }{ 4.36 } = 43.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.49 }{ 62 } = 3.08 ; ;

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{ 59**2-4.36**2-62**2 }{ 2 * 4.36 * 62 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.36**2-59**2-62**2 }{ 2 * 59 * 62 } ) = 2° 59'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 62**2-59**2-4.36**2 }{ 2 * 4.36 * 59 } ) = 132° 26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.49 }{ 62.68 } = 1.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 59 }{ 2 * sin 45° } = 41.72 ; ;





#2 Acute scalene triangle.

Sides: a = 59   b = 83.32547944784   c = 62

Area: T = 1826.505534372
Perimeter: p = 204.3254794478
Semiperimeter: s = 102.1622397239

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 87.00771461392° = 87°26″ = 1.51985611729 rad
Angle ∠ C = γ = 47.99328538608° = 47°59'34″ = 0.83876333173 rad

Height: ha = 61.91554353802
Height: hb = 43.84106204336
Height: hc = 58.92195272166

Median: ma = 67.25551907843
Median: mb = 43.89546996377
Median: mc = 65.219977521

Inradius: r = 17.8788450321
Circumradius: R = 41.719930009

Vertex coordinates: A[62; 0] B[0; 0] C[3.08804727834; 58.92195272166]
Centroid: CG[21.69334909278; 19.64398424055]
Coordinates of the circumscribed circle: U[31; 27.92195272166]
Coordinates of the inscribed circle: I[18.83876027608; 17.8788450321]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 92.99328538608° = 92°59'34″ = 1.51985611729 rad
∠ C' = γ' = 132.0077146139° = 132°26″ = 0.83876333173 rad

Calculate another triangle

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 = 59 ; ; b = 83.32 ; ; c = 62 ; ;

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

p = a+b+c = 59+83.32+62 = 204.32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 204.32 }{ 2 } = 102.16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 102.16 * (102.16-59)(102.16-83.32)(102.16-62) } ; ; T = sqrt{ 3336121.77 } = 1826.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1826.51 }{ 59 } = 61.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1826.51 }{ 83.32 } = 43.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1826.51 }{ 62 } = 58.92 ; ;

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{ 59**2-83.32**2-62**2 }{ 2 * 83.32 * 62 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 83.32**2-59**2-62**2 }{ 2 * 59 * 62 } ) = 87° 26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 62**2-59**2-83.32**2 }{ 2 * 83.32 * 59 } ) = 47° 59'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1826.51 }{ 102.16 } = 17.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 59 }{ 2 * sin 45° } = 41.72 ; ; : Nr. 1




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