Triangle calculator

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

You have entered side a, c and angle α.

Triangle has two solutions: a=52; b=15.87663575253; c=62 and a=52; b=71.80548833418; c=62.

#1 Obtuse scalene triangle.

Sides: a = 52   b = 15.87663575253   c = 62

Area: T = 348.0154682068
Perimeter: p = 129.8766357525
Semiperimeter: s = 64.93881787627

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 12.46877469516° = 12°28'4″ = 0.21876032346 rad
Angle ∠ C = γ = 122.5322253048° = 122°31'56″ = 2.13985912556 rad

Height: ha = 13.38551800795
Height: hb = 43.84106204336
Height: hc = 11.22662800667

Median: ma = 37.04109147314
Median: mb = 56.6665556716
Median: mc = 22.73882797093

Inradius: r = 5.35991691159
Circumradius: R = 36.77695526217

Vertex coordinates: A[62; 0] B[0; 0] C[50.77437199333; 11.22662800667]
Centroid: CG[37.59112399778; 3.74220933556]
Coordinates of the circumscribed circle: U[31; -19.77437199333]
Coordinates of the inscribed circle: I[49.06218212373; 5.35991691159]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 167.5322253048° = 167°31'56″ = 0.21876032346 rad
∠ C' = γ' = 57.46877469516° = 57°28'4″ = 2.13985912556 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 = 52 ; ; b = 15.88 ; ; c = 62 ; ;

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

p = a+b+c = 52+15.88+62 = 129.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 129.88 }{ 2 } = 64.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64.94 * (64.94-52)(64.94-15.88)(64.94-62) } ; ; T = sqrt{ 121114.22 } = 348.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 348.01 }{ 52 } = 13.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 348.01 }{ 15.88 } = 43.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 348.01 }{ 62 } = 11.23 ; ;

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{ 52**2-15.88**2-62**2 }{ 2 * 15.88 * 62 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.88**2-52**2-62**2 }{ 2 * 52 * 62 } ) = 12° 28'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 62**2-52**2-15.88**2 }{ 2 * 15.88 * 52 } ) = 122° 31'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 348.01 }{ 64.94 } = 5.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 52 }{ 2 * sin 45° } = 36.77 ; ;





#2 Acute scalene triangle.

Sides: a = 52   b = 71.80548833418   c = 62

Area: T = 1573.985531793
Perimeter: p = 185.8054883342
Semiperimeter: s = 92.90224416709

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 77.53222530484° = 77°31'56″ = 1.35331930922 rad
Angle ∠ C = γ = 57.46877469516° = 57°28'4″ = 1.0033001398 rad

Height: ha = 60.53878968435
Height: hb = 43.84106204336
Height: hc = 50.77437199333

Median: ma = 61.83882619085
Median: mb = 44.55435035891
Median: mc = 54.48882614502

Inradius: r = 16.94223460743
Circumradius: R = 36.77695526217

Vertex coordinates: A[62; 0] B[0; 0] C[11.22662800667; 50.77437199333]
Centroid: CG[24.40987600222; 16.92545733111]
Coordinates of the circumscribed circle: U[31; 19.77437199333]
Coordinates of the inscribed circle: I[21.09875583291; 16.94223460743]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 102.4687746952° = 102°28'4″ = 1.35331930922 rad
∠ C' = γ' = 122.5322253048° = 122°31'56″ = 1.0033001398 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 = 52 ; ; b = 71.8 ; ; c = 62 ; ;

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

p = a+b+c = 52+71.8+62 = 185.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 185.8 }{ 2 } = 92.9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 92.9 * (92.9-52)(92.9-71.8)(92.9-62) } ; ; T = sqrt{ 2477429.78 } = 1573.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1573.99 }{ 52 } = 60.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1573.99 }{ 71.8 } = 43.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1573.99 }{ 62 } = 50.77 ; ;

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{ 52**2-71.8**2-62**2 }{ 2 * 71.8 * 62 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 71.8**2-52**2-62**2 }{ 2 * 52 * 62 } ) = 77° 31'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 62**2-52**2-71.8**2 }{ 2 * 71.8 * 52 } ) = 57° 28'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1573.99 }{ 92.9 } = 16.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 52 }{ 2 * sin 45° } = 36.77 ; ; : Nr. 1




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