Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 51   b = 56   c = 77

Area: T = 1427.193304931
Perimeter: p = 184
Semiperimeter: s = 92

Angle ∠ A = α = 41.45497838314° = 41°26'59″ = 0.72334352021 rad
Angle ∠ B = β = 46.624394476° = 46°37'26″ = 0.81437413463 rad
Angle ∠ C = γ = 91.92662714086° = 91°55'35″ = 1.60444161052 rad

Height: ha = 55.96883548749
Height: hb = 50.97111803325
Height: hc = 37.07699493327

Median: ma = 62.30877041785
Median: mb = 59
Median: mc = 37.23223783823

Inradius: r = 15.51329679273
Circumradius: R = 38.52217683246

Vertex coordinates: A[77; 0] B[0; 0] C[35.0265974026; 37.07699493327]
Centroid: CG[37.3421991342; 12.35766497776]
Coordinates of the circumscribed circle: U[38.5; -1.29548493554]
Coordinates of the inscribed circle: I[36; 15.51329679273]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5550216169° = 138°33'1″ = 0.72334352021 rad
∠ B' = β' = 133.376605524° = 133°22'34″ = 0.81437413463 rad
∠ C' = γ' = 88.07437285914° = 88°4'25″ = 1.60444161052 rad

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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 = 51 ; ; b = 56 ; ; c = 77 ; ;

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

p = a+b+c = 51+56+77 = 184 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 184 }{ 2 } = 92 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 92 * (92-51)(92-56)(92-77) } ; ; T = sqrt{ 2036880 } = 1427.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1427.19 }{ 51 } = 55.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1427.19 }{ 56 } = 50.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1427.19 }{ 77 } = 37.07 ; ;

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{ 51**2-56**2-77**2 }{ 2 * 56 * 77 } ) = 41° 26'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 56**2-51**2-77**2 }{ 2 * 51 * 77 } ) = 46° 37'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 77**2-51**2-56**2 }{ 2 * 56 * 51 } ) = 91° 55'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1427.19 }{ 92 } = 15.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 51 }{ 2 * sin 41° 26'59" } = 38.52 ; ;




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