Triangle calculator

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

You have entered side b, c and angle β.

Triangle has two solutions: a=1943.679902616; b=850; c=2450 and a=2716.498790369; b=850; c=2450.

#1 Obtuse scalene triangle.

Sides: a = 1943.679902616   b = 850   c = 2450

Area: T = 735771.5677098
Perimeter: p = 5243.679902616
Semiperimeter: s = 2621.843951308

Angle ∠ A = α = 44.96108419936° = 44°57'39″ = 0.78547147273 rad
Angle ∠ B = β = 18° = 0.31441592654 rad
Angle ∠ C = γ = 117.0399158006° = 117°2'21″ = 2.0432718661 rad

Height: ha = 757.0921636219
Height: hb = 1731.22772167
Height: hc = 600.6329850693

Median: ma = 1555.001095203
Median: mb = 2170.154416005
Median: mc = 865.7776575313

Inradius: r = 280.6321809624
Circumradius: R = 1375.329889044

Vertex coordinates: A[2450; 0] B[0; 0] C[1848.549860341; 600.6329850693]
Centroid: CG[1432.854953447; 200.2109950231]
Coordinates of the circumscribed circle: U[1225; -625.2243605498]
Coordinates of the inscribed circle: I[1771.843951308; 280.6321809624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0399158006° = 135°2'21″ = 0.78547147273 rad
∠ B' = β' = 162° = 0.31441592654 rad
∠ C' = γ' = 62.96108419936° = 62°57'39″ = 2.0432718661 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 = 1943.68 ; ; b = 850 ; ; c = 2450 ; ;

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

p = a+b+c = 1943.68+850+2450 = 5243.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5243.68 }{ 2 } = 2621.84 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2621.84 * (2621.84-1943.68)(2621.84-850)(2621.84-2450) } ; ; T = sqrt{ 541359798950 } = 735771.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 735771.57 }{ 1943.68 } = 757.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 735771.57 }{ 850 } = 1731.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 735771.57 }{ 2450 } = 600.63 ; ;

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{ 1943.68**2-850**2-2450**2 }{ 2 * 850 * 2450 } ) = 44° 57'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 850**2-1943.68**2-2450**2 }{ 2 * 1943.68 * 2450 } ) = 18° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2450**2-1943.68**2-850**2 }{ 2 * 850 * 1943.68 } ) = 117° 2'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 735771.57 }{ 2621.84 } = 280.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1943.68 }{ 2 * sin 44° 57'39" } = 1375.33 ; ;





#2 Obtuse scalene triangle.

Sides: a = 2716.498790369   b = 850   c = 2450

Area: T = 1028318.921134
Perimeter: p = 6016.498790369
Semiperimeter: s = 3008.249895184

Angle ∠ A = α = 99.03991580064° = 99°2'21″ = 1.72985593956 rad
Angle ∠ B = β = 18° = 0.31441592654 rad
Angle ∠ C = γ = 62.96108419936° = 62°57'39″ = 1.09988739926 rad

Height: ha = 757.0921636219
Height: hb = 2419.574393258
Height: hc = 839.4444017424

Median: ma = 1231.933335242
Median: mb = 2551.533001753
Median: mc = 1596.968757336

Inradius: r = 341.8333052319
Circumradius: R = 1375.329889044

Vertex coordinates: A[2450; 0] B[0; 0] C[2583.543303281; 839.4444017424]
Centroid: CG[1677.84876776; 279.8154672475]
Coordinates of the circumscribed circle: U[1225; 625.2243605498]
Coordinates of the inscribed circle: I[2158.249895184; 341.8333052319]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 80.96108419936° = 80°57'39″ = 1.72985593956 rad
∠ B' = β' = 162° = 0.31441592654 rad
∠ C' = γ' = 117.0399158006° = 117°2'21″ = 1.09988739926 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 = 2716.5 ; ; b = 850 ; ; c = 2450 ; ;

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

p = a+b+c = 2716.5+850+2450 = 6016.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6016.5 }{ 2 } = 3008.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3008.25 * (3008.25-2716.5)(3008.25-850)(3008.25-2450) } ; ; T = sqrt{ 1.057 * 10**{ 12 } } = 1028318.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1028318.92 }{ 2716.5 } = 757.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1028318.92 }{ 850 } = 2419.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1028318.92 }{ 2450 } = 839.44 ; ;

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{ 2716.5**2-850**2-2450**2 }{ 2 * 850 * 2450 } ) = 99° 2'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 850**2-2716.5**2-2450**2 }{ 2 * 2716.5 * 2450 } ) = 18° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2450**2-2716.5**2-850**2 }{ 2 * 850 * 2716.5 } ) = 62° 57'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1028318.92 }{ 3008.25 } = 341.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2716.5 }{ 2 * sin 99° 2'21" } = 1375.33 ; ;




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