Triangle calculator

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

You have entered side a, b and angle β.

Triangle has two solutions: a=38.3; b=33.1; c=6.68875556733 and a=38.3; b=33.1; c=55.51880424867.

#1 Obtuse scalene triangle.

Sides: a = 38.3   b = 33.1   c = 6.68875556733

Area: T = 74.73221920839
Perimeter: p = 78.08875556733
Semiperimeter: s = 39.04437778366

Angle ∠ A = α = 137.5299123672° = 137°31'45″ = 2.44003360255 rad
Angle ∠ B = β = 35.7° = 35°42' = 0.6233082543 rad
Angle ∠ C = γ = 6.77108763283° = 6°46'15″ = 0.11881740852 rad

Height: ha = 3.90224643386
Height: hb = 4.51655403072
Height: hc = 22.35496283949

Median: ma = 14.26333867101
Median: mb = 21.95223165165
Median: mc = 35.6388029544

Inradius: r = 1.91440615029
Circumradius: R = 28.36113216649

Vertex coordinates: A[6.68875556733; 0] B[0; 0] C[31.103279908; 22.35496283949]
Centroid: CG[12.59767849177; 7.45498761316]
Coordinates of the circumscribed circle: U[3.34437778366; 28.16435174714]
Coordinates of the inscribed circle: I[5.94437778366; 1.91440615029]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.47108763283° = 42°28'15″ = 2.44003360255 rad
∠ B' = β' = 144.3° = 144°18' = 0.6233082543 rad
∠ C' = γ' = 173.2299123672° = 173°13'45″ = 0.11881740852 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 = 38.3 ; ; b = 33.1 ; ; c = 6.69 ; ;

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

p = a+b+c = 38.3+33.1+6.69 = 78.09 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78.09 }{ 2 } = 39.04 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.04 * (39.04-38.3)(39.04-33.1)(39.04-6.69) } ; ; T = sqrt{ 5584.9 } = 74.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.73 }{ 38.3 } = 3.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.73 }{ 33.1 } = 4.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.73 }{ 6.69 } = 22.35 ; ;

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{ 38.3**2-33.1**2-6.69**2 }{ 2 * 33.1 * 6.69 } ) = 137° 31'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 33.1**2-38.3**2-6.69**2 }{ 2 * 38.3 * 6.69 } ) = 35° 42' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.69**2-38.3**2-33.1**2 }{ 2 * 33.1 * 38.3 } ) = 6° 46'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.73 }{ 39.04 } = 1.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38.3 }{ 2 * sin 137° 31'45" } = 28.36 ; ;





#2 Obtuse scalene triangle.

Sides: a = 38.3   b = 33.1   c = 55.51880424867

Area: T = 620.4043809396
Perimeter: p = 126.9188042487
Semiperimeter: s = 63.45990212433

Angle ∠ A = α = 42.47108763283° = 42°28'15″ = 0.74112566281 rad
Angle ∠ B = β = 35.7° = 35°42' = 0.6233082543 rad
Angle ∠ C = γ = 101.8299123672° = 101°49'45″ = 1.77772534825 rad

Height: ha = 32.39770657648
Height: hb = 37.48766350088
Height: hc = 22.35496283949

Median: ma = 41.54995062715
Median: mb = 44.72988388042
Median: mc = 22.59883791368

Inradius: r = 9.77664478122
Circumradius: R = 28.36113216649

Vertex coordinates: A[55.51880424867; 0] B[0; 0] C[31.103279908; 22.35496283949]
Centroid: CG[28.87436138555; 7.45498761316]
Coordinates of the circumscribed circle: U[27.75990212433; -5.81438890764]
Coordinates of the inscribed circle: I[30.35990212433; 9.77664478122]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.5299123672° = 137°31'45″ = 0.74112566281 rad
∠ B' = β' = 144.3° = 144°18' = 0.6233082543 rad
∠ C' = γ' = 78.17108763283° = 78°10'15″ = 1.77772534825 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 = 38.3 ; ; b = 33.1 ; ; c = 55.52 ; ;

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

p = a+b+c = 38.3+33.1+55.52 = 126.92 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 126.92 }{ 2 } = 63.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 63.46 * (63.46-38.3)(63.46-33.1)(63.46-55.52) } ; ; T = sqrt{ 384900.89 } = 620.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 620.4 }{ 38.3 } = 32.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 620.4 }{ 33.1 } = 37.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 620.4 }{ 55.52 } = 22.35 ; ;

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{ 38.3**2-33.1**2-55.52**2 }{ 2 * 33.1 * 55.52 } ) = 42° 28'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 33.1**2-38.3**2-55.52**2 }{ 2 * 38.3 * 55.52 } ) = 35° 42' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 55.52**2-38.3**2-33.1**2 }{ 2 * 33.1 * 38.3 } ) = 101° 49'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 620.4 }{ 63.46 } = 9.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38.3 }{ 2 * sin 42° 28'15" } = 28.36 ; ;




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