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=149600000; b=57910000; c=101439971.751 and a=149600000; b=57910000; c=187565035.475.

#1 Obtuse scalene triangle.

Sides: a = 149600000   b = 57910000   c = 101439971.751

Area: T = 1.96384382746E+15
Perimeter: p = 308949971.751
Semiperimeter: s = 154474985.875

Angle ∠ A = α = 138.0439960574° = 138°2'24″ = 2.40992518113 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 26.96600394264° = 26°57'36″ = 0.47105414545 rad

Height: ha = 26254596.62437
Height: hb = 67823996.80439
Height: hc = 38719329.14773

Median: ma = 35025390.56773
Median: mb = 124485830.155
Median: mc = 101461061.905

Inradius: r = 12713021.57
Circumradius: R = 111873529.201

Vertex coordinates: A[101439971.751; 0] B[0; 0] C[144502503.613; 38719329.14773]
Centroid: CG[81980825.12112; 12906443.04991]
Coordinates of the circumscribed circle: U[50719985.87553; 99715442.98797]
Coordinates of the inscribed circle: I[96564985.87553; 12713021.57]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 41.96600394264° = 41°57'36″ = 2.40992518113 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 153.0439960574° = 153°2'24″ = 0.47105414545 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 = 149600000 ; ; b = 57910000 ; ; c = 101439971.75 ; ;

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

p = a+b+c = 149600000+57910000+101439971.75 = 308949971.75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 308949971.75 }{ 2 } = 154474985.88 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 154474985.88 * (154474985.88-149600000)(154474985.88-57910000)(154474985.88-101439971.75) } ; ; T = sqrt{ 3.857 * 10**{ 30 } } = 1.964 * 10**{ 15 } ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.964 * 10**{ 15 } }{ 149600000 } = 26254596.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.964 * 10**{ 15 } }{ 57910000 } = 67823996.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.964 * 10**{ 15 } }{ 101439971.75 } = 38719329.15 ; ;

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{ 149600000**2-57910000**2-101439971.75**2 }{ 2 * 57910000 * 101439971.75 } ) = 138° 2'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 57910000**2-149600000**2-101439971.75**2 }{ 2 * 149600000 * 101439971.75 } ) = 15° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 101439971.75**2-149600000**2-57910000**2 }{ 2 * 57910000 * 149600000 } ) = 26° 57'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.964 * 10**{ 15 } }{ 154474985.88 } = 12713021.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 149600000 }{ 2 * sin 138° 2'24" } = 111873529.2 ; ;





#2 Obtuse scalene triangle.

Sides: a = 149600000   b = 57910000   c = 187565035.475

Area: T = 3.63119617254E+15
Perimeter: p = 395075035.475
Semiperimeter: s = 197537517.738

Angle ∠ A = α = 41.96600394264° = 41°57'36″ = 0.73223408423 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 123.0439960574° = 123°2'24″ = 2.14774524235 rad

Height: ha = 48545403.37663
Height: hb = 125408260.147
Height: hc = 38719329.14773

Median: ma = 116927607.161
Median: mb = 167158634.959
Median: mc = 63809900.61775

Inradius: r = 18382311.44221
Circumradius: R = 111873529.201

Vertex coordinates: A[187565035.475; 0] B[0; 0] C[144502503.613; 38719329.14773]
Centroid: CG[110689179.696; 12906443.04991]
Coordinates of the circumscribed circle: U[93782517.73875; -60996113.83224]
Coordinates of the inscribed circle: I[139627517.738; 18382311.44221]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0439960574° = 138°2'24″ = 0.73223408423 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 56.96600394264° = 56°57'36″ = 2.14774524235 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 = 149600000 ; ; b = 57910000 ; ; c = 187565035.48 ; ;

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

p = a+b+c = 149600000+57910000+187565035.48 = 395075035.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 395075035.48 }{ 2 } = 197537517.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 197537517.74 * (197537517.74-149600000)(197537517.74-57910000)(197537517.74-187565035.48) } ; ; T = sqrt{ 1.319 * 10**{ 31 } } = 3.631 * 10**{ 15 } ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.631 * 10**{ 15 } }{ 149600000 } = 48545403.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.631 * 10**{ 15 } }{ 57910000 } = 125408260.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.631 * 10**{ 15 } }{ 187565035.48 } = 38719329.15 ; ;

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{ 149600000**2-57910000**2-187565035.48**2 }{ 2 * 57910000 * 187565035.48 } ) = 41° 57'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 57910000**2-149600000**2-187565035.48**2 }{ 2 * 149600000 * 187565035.48 } ) = 15° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 187565035.48**2-149600000**2-57910000**2 }{ 2 * 57910000 * 149600000 } ) = 123° 2'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.631 * 10**{ 15 } }{ 197537517.74 } = 18382311.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 149600000 }{ 2 * sin 41° 57'36" } = 111873529.2 ; ;




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