Triangle calculator

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

You have entered side b, c and angle γ.

Triangle has two solutions: a=2.49329557658; b=20.2; c=18.3 and a=29.34326786799; b=20.2; c=18.3.

#1 Obtuse scalene triangle.

Sides: a = 2.49329557658   b = 20.2   c = 18.3

Area: T = 15.50216499296
Perimeter: p = 40.99329557658
Semiperimeter: s = 20.49664778829

Angle ∠ A = α = 4.81110354856° = 4°48'40″ = 0.08439684097 rad
Angle ∠ B = β = 137.1898964514° = 137°11'20″ = 2.39443991282 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 12.43663618016
Height: hb = 1.53548168247
Height: hc = 1.69441693912

Median: ma = 19.23330780919
Median: mb = 8.27990346192
Median: mc = 11.10987764504

Inradius: r = 0.75663079871
Circumradius: R = 14.86220635962

Vertex coordinates: A[18.3; 0] B[0; 0] C[-1.82988298238; 1.69441693912]
Centroid: CG[5.49903900587; 0.56547231304]
Coordinates of the circumscribed circle: U[9.15; 11.71114659346]
Coordinates of the inscribed circle: I[0.29664778829; 0.75663079871]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.1898964514° = 175°11'20″ = 0.08439684097 rad
∠ B' = β' = 42.81110354856° = 42°48'40″ = 2.39443991282 rad
∠ C' = γ' = 142° = 0.66332251158 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 = 2.49 ; ; b = 20.2 ; ; c = 18.3 ; ;

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

p = a+b+c = 2.49+20.2+18.3 = 40.99 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40.99 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-2.49)(20.5-20.2)(20.5-18.3) } ; ; T = sqrt{ 240.3 } = 15.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.5 }{ 2.49 } = 12.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.5 }{ 20.2 } = 1.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.5 }{ 18.3 } = 1.69 ; ;

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{ 2.49**2-20.2**2-18.3**2 }{ 2 * 20.2 * 18.3 } ) = 4° 48'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20.2**2-2.49**2-18.3**2 }{ 2 * 2.49 * 18.3 } ) = 137° 11'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18.3**2-2.49**2-20.2**2 }{ 2 * 20.2 * 2.49 } ) = 38° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.5 }{ 20.5 } = 0.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.49 }{ 2 * sin 4° 48'40" } = 14.86 ; ;





#2 Obtuse scalene triangle.

Sides: a = 29.34326786799   b = 20.2   c = 18.3

Area: T = 182.4588084145
Perimeter: p = 67.84326786799
Semiperimeter: s = 33.92113393399

Angle ∠ A = α = 99.18989645144° = 99°11'20″ = 1.73111740124 rad
Angle ∠ B = β = 42.81110354856° = 42°48'40″ = 0.74771935254 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 12.43663618016
Height: hb = 18.06551568461
Height: hc = 19.94107742235

Median: ma = 12.49986720084
Median: mb = 22.2769517194
Median: mc = 23.46989986164

Inradius: r = 5.37988584913
Circumradius: R = 14.86220635962

Vertex coordinates: A[18.3; 0] B[0; 0] C[21.52657593473; 19.94107742235]
Centroid: CG[13.27552531158; 6.64769247412]
Coordinates of the circumscribed circle: U[9.15; 11.71114659346]
Coordinates of the inscribed circle: I[13.72113393399; 5.37988584913]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 80.81110354856° = 80°48'40″ = 1.73111740124 rad
∠ B' = β' = 137.1898964514° = 137°11'20″ = 0.74771935254 rad
∠ C' = γ' = 142° = 0.66332251158 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 = 29.34 ; ; b = 20.2 ; ; c = 18.3 ; ;

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

p = a+b+c = 29.34+20.2+18.3 = 67.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67.84 }{ 2 } = 33.92 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.92 * (33.92-29.34)(33.92-20.2)(33.92-18.3) } ; ; T = sqrt{ 33290.95 } = 182.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 182.46 }{ 29.34 } = 12.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 182.46 }{ 20.2 } = 18.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 182.46 }{ 18.3 } = 19.94 ; ;

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{ 29.34**2-20.2**2-18.3**2 }{ 2 * 20.2 * 18.3 } ) = 99° 11'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20.2**2-29.34**2-18.3**2 }{ 2 * 29.34 * 18.3 } ) = 42° 48'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18.3**2-29.34**2-20.2**2 }{ 2 * 20.2 * 29.34 } ) = 38° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 182.46 }{ 33.92 } = 5.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 29.34 }{ 2 * sin 99° 11'20" } = 14.86 ; ;




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