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=155; b=63; c=99.77106663709 and a=155; b=63; c=201.0211008775.

#1 Obtuse scalene triangle.

Sides: a = 155   b = 63   c = 99.77106663709

Area: T = 1870.595492686
Perimeter: p = 317.7710666371
Semiperimeter: s = 158.8855333186

Angle ∠ A = α = 143.4732776509° = 143°28'22″ = 2.50440723371 rad
Angle ∠ B = β = 14° = 0.24443460953 rad
Angle ∠ C = γ = 22.52772234906° = 22°31'38″ = 0.39331742212 rad

Height: ha = 24.13767087337
Height: hb = 59.38439659321
Height: hc = 37.49878938179

Median: ma = 30.90986223253
Median: mb = 126.4810602995
Median: mc = 107.2777460508

Inradius: r = 11.77332385322
Circumradius: R = 130.2077313075

Vertex coordinates: A[99.77106663709; 0] B[0; 0] C[150.3965837573; 37.49878938179]
Centroid: CG[83.38988346479; 12.49992979393]
Coordinates of the circumscribed circle: U[49.88553331855; 120.2722182616]
Coordinates of the inscribed circle: I[95.88553331855; 11.77332385322]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 36.52772234906° = 36°31'38″ = 2.50440723371 rad
∠ B' = β' = 166° = 0.24443460953 rad
∠ C' = γ' = 157.4732776509° = 157°28'22″ = 0.39331742212 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 = 155 ; ; b = 63 ; ; c = 99.77 ; ;

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

p = a+b+c = 155+63+99.77 = 317.77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 317.77 }{ 2 } = 158.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 158.89 * (158.89-155)(158.89-63)(158.89-99.77) } ; ; T = sqrt{ 3499125.38 } = 1870.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1870.59 }{ 155 } = 24.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1870.59 }{ 63 } = 59.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1870.59 }{ 99.77 } = 37.5 ; ;

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{ 155**2-63**2-99.77**2 }{ 2 * 63 * 99.77 } ) = 143° 28'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 63**2-155**2-99.77**2 }{ 2 * 155 * 99.77 } ) = 14° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 99.77**2-155**2-63**2 }{ 2 * 63 * 155 } ) = 22° 31'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1870.59 }{ 158.89 } = 11.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 155 }{ 2 * sin 143° 28'22" } = 130.21 ; ;





#2 Obtuse scalene triangle.

Sides: a = 155   b = 63   c = 201.0211008775

Area: T = 3768.93222211
Perimeter: p = 419.0211008775
Semiperimeter: s = 209.5110504387

Angle ∠ A = α = 36.52772234906° = 36°31'38″ = 0.63875203165 rad
Angle ∠ B = β = 14° = 0.24443460953 rad
Angle ∠ C = γ = 129.4732776509° = 129°28'22″ = 2.26597262418 rad

Height: ha = 48.63113834981
Height: hb = 119.649864194
Height: hc = 37.49878938179

Median: ma = 127.2122314594
Median: mb = 176.7065894028
Median: mc = 62.40770389284

Inradius: r = 17.98992279489
Circumradius: R = 130.2077313075

Vertex coordinates: A[201.0211008775; 0] B[0; 0] C[150.3965837573; 37.49878938179]
Centroid: CG[117.1398948782; 12.49992979393]
Coordinates of the circumscribed circle: U[100.5110504387; -82.77442887977]
Coordinates of the inscribed circle: I[146.5110504387; 17.98992279489]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.4732776509° = 143°28'22″ = 0.63875203165 rad
∠ B' = β' = 166° = 0.24443460953 rad
∠ C' = γ' = 50.52772234906° = 50°31'38″ = 2.26597262418 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 = 155 ; ; b = 63 ; ; c = 201.02 ; ;

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

p = a+b+c = 155+63+201.02 = 419.02 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 419.02 }{ 2 } = 209.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 209.51 * (209.51-155)(209.51-63)(209.51-201.02) } ; ; T = sqrt{ 14204850.09 } = 3768.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3768.93 }{ 155 } = 48.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3768.93 }{ 63 } = 119.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3768.93 }{ 201.02 } = 37.5 ; ;

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{ 155**2-63**2-201.02**2 }{ 2 * 63 * 201.02 } ) = 36° 31'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 63**2-155**2-201.02**2 }{ 2 * 155 * 201.02 } ) = 14° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 201.02**2-155**2-63**2 }{ 2 * 63 * 155 } ) = 129° 28'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3768.93 }{ 209.51 } = 17.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 155 }{ 2 * sin 36° 31'38" } = 130.21 ; ;




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