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=73; b=63; c=11.23113542608 and a=73; b=63; c=121.0989582647.

#1 Obtuse scalene triangle.

Sides: a = 73   b = 63   c = 11.23113542608

Area: T = 173.2550002637
Perimeter: p = 147.2311354261
Semiperimeter: s = 73.61656771304

Angle ∠ A = α = 150.6799100112° = 150°40'45″ = 2.63298464109 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 4.32108998877° = 4°19'15″ = 0.07554139297 rad

Height: ha = 4.74765754147
Height: hb = 5.55000000837
Height: hc = 30.85111331071

Median: ma = 26.74554979252
Median: mb = 41.65771921673
Median: mc = 67.95219254353

Inradius: r = 2.35334389602
Circumradius: R = 74.53553498693

Vertex coordinates: A[11.23113542608; 0] B[0; 0] C[66.16604684537; 30.85111331071]
Centroid: CG[25.79772742382; 10.28437110357]
Coordinates of the circumscribed circle: U[5.61656771304; 74.32334993155]
Coordinates of the inscribed circle: I[10.61656771304; 2.35334389602]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.32108998877° = 29°19'15″ = 2.63298464109 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 175.6799100112° = 175°40'45″ = 0.07554139297 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 = 73 ; ; b = 63 ; ; c = 11.23 ; ;

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

p = a+b+c = 73+63+11.23 = 147.23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 147.23 }{ 2 } = 73.62 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 73.62 * (73.62-73)(73.62-63)(73.62-11.23) } ; ; T = sqrt{ 30015.56 } = 173.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 173.25 }{ 73 } = 4.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 173.25 }{ 63 } = 5.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 173.25 }{ 11.23 } = 30.85 ; ;

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{ 73**2-63**2-11.23**2 }{ 2 * 63 * 11.23 } ) = 150° 40'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 63**2-73**2-11.23**2 }{ 2 * 73 * 11.23 } ) = 25° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.23**2-73**2-63**2 }{ 2 * 63 * 73 } ) = 4° 19'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 173.25 }{ 73.62 } = 2.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 73 }{ 2 * sin 150° 40'45" } = 74.54 ; ;





#2 Obtuse scalene triangle.

Sides: a = 73   b = 63   c = 121.0989582647

Area: T = 1867.875541605
Perimeter: p = 257.0989582646
Semiperimeter: s = 128.5454791323

Angle ∠ A = α = 29.32108998877° = 29°19'15″ = 0.51217462427 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 125.6799100112° = 125°40'45″ = 2.19435140979 rad

Height: ha = 51.1754668933
Height: hb = 59.29876322557
Height: hc = 30.85111331071

Median: ma = 89.35109569773
Median: mb = 94.88772673901
Median: mc = 31.35880650491

Inradius: r = 14.53109304004
Circumradius: R = 74.53553498693

Vertex coordinates: A[121.0989582647; 0] B[0; 0] C[66.16604684537; 30.85111331071]
Centroid: CG[62.41766837001; 10.28437110357]
Coordinates of the circumscribed circle: U[60.54547913233; -43.47223662085]
Coordinates of the inscribed circle: I[65.54547913233; 14.53109304004]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.6799100112° = 150°40'45″ = 0.51217462427 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 54.32108998877° = 54°19'15″ = 2.19435140979 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 = 73 ; ; b = 63 ; ; c = 121.09 ; ;

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

p = a+b+c = 73+63+121.09 = 257.09 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 257.09 }{ 2 } = 128.54 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 128.54 * (128.54-73)(128.54-63)(128.54-121.09) } ; ; T = sqrt{ 3488958.57 } = 1867.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1867.88 }{ 73 } = 51.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1867.88 }{ 63 } = 59.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1867.88 }{ 121.09 } = 30.85 ; ;

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{ 73**2-63**2-121.09**2 }{ 2 * 63 * 121.09 } ) = 29° 19'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 63**2-73**2-121.09**2 }{ 2 * 73 * 121.09 } ) = 25° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 121.09**2-73**2-63**2 }{ 2 * 63 * 73 } ) = 125° 40'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1867.88 }{ 128.54 } = 14.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 73 }{ 2 * sin 29° 19'15" } = 74.54 ; ;




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