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 = 98   b = 76   c = 57

Area: T = 2161.158789277
Perimeter: p = 231
Semiperimeter: s = 115.5

Angle ∠ A = α = 93.83218327432° = 93°49'55″ = 1.63876744245 rad
Angle ∠ B = β = 50.69442413116° = 50°41'39″ = 0.88547814227 rad
Angle ∠ C = γ = 35.47439259452° = 35°28'26″ = 0.61991368064 rad

Height: ha = 44.10552631178
Height: hb = 56.87325761256
Height: hc = 75.83301015008

Median: ma = 45.95110609236
Median: mb = 70.58768259663
Median: mc = 82.93222012249

Inradius: r = 18.7111323747
Circumradius: R = 49.11097852475

Vertex coordinates: A[57; 0] B[0; 0] C[62.07989473684; 75.83301015008]
Centroid: CG[39.69329824561; 25.27767005003]
Coordinates of the circumscribed circle: U[28.5; 39.994401214]
Coordinates of the inscribed circle: I[39.5; 18.7111323747]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 86.16881672568° = 86°10'5″ = 1.63876744245 rad
∠ B' = β' = 129.3065758688° = 129°18'21″ = 0.88547814227 rad
∠ C' = γ' = 144.5266074055° = 144°31'34″ = 0.61991368064 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 = 98 ; ; b = 76 ; ; c = 57 ; ;

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

p = a+b+c = 98+76+57 = 231 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 231 }{ 2 } = 115.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 115.5 * (115.5-98)(115.5-76)(115.5-57) } ; ; T = sqrt{ 4670603.44 } = 2161.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2161.16 }{ 98 } = 44.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2161.16 }{ 76 } = 56.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2161.16 }{ 57 } = 75.83 ; ;

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{ 98**2-76**2-57**2 }{ 2 * 76 * 57 } ) = 93° 49'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 76**2-98**2-57**2 }{ 2 * 98 * 57 } ) = 50° 41'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 57**2-98**2-76**2 }{ 2 * 76 * 98 } ) = 35° 28'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2161.16 }{ 115.5 } = 18.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 98 }{ 2 * sin 93° 49'55" } = 49.11 ; ;




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