Triangle calculator - result

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

You have entered side a, area T and angle β.

Obtuse scalene triangle.

Sides: a = 3   b = 16.26601938325   c = 18.93296126652

Area: T = 12
Perimeter: p = 38.19898064977
Semiperimeter: s = 19.09549032489

Angle ∠ A = α = 4.4722058555° = 4°28'19″ = 0.07880521461 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 150.5287941445° = 150°31'41″ = 2.62772081945 rad

Height: ha = 8
Height: hb = 1.47659971651
Height: hc = 1.26878547852

Median: ma = 17.58215832496
Median: mb = 10.8432815223
Median: mc = 6.86439924841

Inradius: r = 0.62884399477
Circumradius: R = 19.23774481944

Vertex coordinates: A[18.93296126652; 0] B[0; 0] C[2.71989233611; 1.26878547852]
Centroid: CG[7.21661786754; 0.42326182617]
Coordinates of the circumscribed circle: U[9.46548063326; -16.74880403068]
Coordinates of the inscribed circle: I[2.83547094164; 0.62884399477]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5287941445° = 175°31'41″ = 0.07880521461 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 29.4722058555° = 29°28'19″ = 2.62772081945 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 = 3 ; ; b = 16.26 ; ; c = 18.93 ; ;

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

p = a+b+c = 3+16.26+18.93 = 38.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38.19 }{ 2 } = 19.09 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.09 * (19.09-3)(19.09-16.26)(19.09-18.93) } ; ; T = sqrt{ 144 } = 12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12 }{ 3 } = 8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12 }{ 16.26 } = 1.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12 }{ 18.93 } = 1.27 ; ;

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{ 3**2-16.26**2-18.93**2 }{ 2 * 16.26 * 18.93 } ) = 4° 28'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16.26**2-3**2-18.93**2 }{ 2 * 3 * 18.93 } ) = 25° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18.93**2-3**2-16.26**2 }{ 2 * 16.26 * 3 } ) = 150° 31'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12 }{ 19.09 } = 0.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 4° 28'19" } = 19.24 ; ;




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