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=3.79662124427; b=35; c=38 and a=57.68990791298; b=35; c=38.

#1 Obtuse scalene triangle.

Sides: a = 3.79662124427   b = 35   c = 38

Area: T = 42.39657960793
Perimeter: p = 76.79662124427
Semiperimeter: s = 38.39881062213

Angle ∠ A = α = 3.6555261197° = 3°39'19″ = 0.06437963429 rad
Angle ∠ B = β = 36° = 0.62883185307 rad
Angle ∠ C = γ = 140.3454738803° = 140°20'41″ = 2.449947778 rad

Height: ha = 22.33658395871
Height: hb = 2.42326169188
Height: hc = 2.23113576884

Median: ma = 36.48114636874
Median: mb = 20.56658847234
Median: mc = 16.08443282252

Inradius: r = 1.10441116412
Circumradius: R = 29.77327782923

Vertex coordinates: A[38; 0] B[0; 0] C[3.07112003804; 2.23113576884]
Centroid: CG[13.69904001268; 0.74437858961]
Coordinates of the circumscribed circle: U[19; -22.92220053059]
Coordinates of the inscribed circle: I[3.39881062213; 1.10441116412]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.3454738803° = 176°20'41″ = 0.06437963429 rad
∠ B' = β' = 144° = 0.62883185307 rad
∠ C' = γ' = 39.6555261197° = 39°39'19″ = 2.449947778 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 = 3.8 ; ; b = 35 ; ; c = 38 ; ;

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

p = a+b+c = 3.8+35+38 = 76.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76.8 }{ 2 } = 38.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.4 * (38.4-3.8)(38.4-35)(38.4-38) } ; ; T = sqrt{ 1797.4 } = 42.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.4 }{ 3.8 } = 22.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.4 }{ 35 } = 2.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.4 }{ 38 } = 2.23 ; ;

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{ 3.8**2-35**2-38**2 }{ 2 * 35 * 38 } ) = 3° 39'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 35**2-3.8**2-38**2 }{ 2 * 3.8 * 38 } ) = 36° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 38**2-3.8**2-35**2 }{ 2 * 35 * 3.8 } ) = 140° 20'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.4 }{ 38.4 } = 1.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.8 }{ 2 * sin 3° 39'19" } = 29.77 ; ;





#2 Obtuse scalene triangle.

Sides: a = 57.68990791298   b = 35   c = 38

Area: T = 644.2677008686
Perimeter: p = 130.689907913
Semiperimeter: s = 65.34545395649

Angle ∠ A = α = 104.3454738803° = 104°20'41″ = 1.82111592492 rad
Angle ∠ B = β = 36° = 0.62883185307 rad
Angle ∠ C = γ = 39.6555261197° = 39°39'19″ = 0.69221148736 rad

Height: ha = 22.33658395871
Height: hb = 36.81552576392
Height: hc = 33.90987899308

Median: ma = 22.41663453152
Median: mb = 45.60444397556
Median: mc = 43.76765959999

Inradius: r = 9.86595385778
Circumradius: R = 29.77327782923

Vertex coordinates: A[38; 0] B[0; 0] C[46.67114454059; 33.90987899308]
Centroid: CG[28.22438151353; 11.30329299769]
Coordinates of the circumscribed circle: U[19; 22.92220053059]
Coordinates of the inscribed circle: I[30.34545395649; 9.86595385778]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 75.6555261197° = 75°39'19″ = 1.82111592492 rad
∠ B' = β' = 144° = 0.62883185307 rad
∠ C' = γ' = 140.3454738803° = 140°20'41″ = 0.69221148736 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 = 57.69 ; ; b = 35 ; ; c = 38 ; ;

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

p = a+b+c = 57.69+35+38 = 130.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 130.69 }{ 2 } = 65.34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 65.34 * (65.34-57.69)(65.34-35)(65.34-38) } ; ; T = sqrt{ 415079.98 } = 644.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 644.27 }{ 57.69 } = 22.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 644.27 }{ 35 } = 36.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 644.27 }{ 38 } = 33.91 ; ;

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{ 57.69**2-35**2-38**2 }{ 2 * 35 * 38 } ) = 104° 20'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 35**2-57.69**2-38**2 }{ 2 * 57.69 * 38 } ) = 36° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 38**2-57.69**2-35**2 }{ 2 * 35 * 57.69 } ) = 39° 39'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 644.27 }{ 65.34 } = 9.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 57.69 }{ 2 * sin 104° 20'41" } = 29.77 ; ;




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