Triangle calculator

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

You have entered side a, angle α and angle γ.

Obtuse scalene triangle.

Sides: a = 10.2   b = 15.55334998432   c = 7.79656230659

Area: T = 34.77328483704
Perimeter: p = 33.5499122909
Semiperimeter: s = 16.77545614545

Angle ∠ A = α = 35° = 0.61108652382 rad
Angle ∠ B = β = 119° = 2.07769418099 rad
Angle ∠ C = γ = 26° = 0.45437856055 rad

Height: ha = 6.81882055628
Height: hb = 4.47113856972
Height: hc = 8.92111210128

Median: ma = 11.19551573539
Median: mb = 4.68327374632
Median: mc = 12.56111601351

Inradius: r = 2.0732951264
Circumradius: R = 8.89215786577

Vertex coordinates: A[7.79656230659; 0] B[0; 0] C[-4.94550581265; 8.92111210128]
Centroid: CG[0.95501883131; 2.97437070043]
Coordinates of the circumscribed circle: U[3.89878115329; 7.99216979597]
Coordinates of the inscribed circle: I[1.22110616114; 2.0732951264]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145° = 0.61108652382 rad
∠ B' = β' = 61° = 2.07769418099 rad
∠ C' = γ' = 154° = 0.45437856055 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 = 10.2 ; ; b = 15.55 ; ; c = 7.8 ; ;

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

p = a+b+c = 10.2+15.55+7.8 = 33.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.55 }{ 2 } = 16.77 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.77 * (16.77-10.2)(16.77-15.55)(16.77-7.8) } ; ; T = sqrt{ 1209.15 } = 34.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.77 }{ 10.2 } = 6.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.77 }{ 15.55 } = 4.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.77 }{ 7.8 } = 8.92 ; ;

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{ 10.2**2-15.55**2-7.8**2 }{ 2 * 15.55 * 7.8 } ) = 35° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.55**2-10.2**2-7.8**2 }{ 2 * 10.2 * 7.8 } ) = 119° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.8**2-10.2**2-15.55**2 }{ 2 * 15.55 * 10.2 } ) = 26° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.77 }{ 16.77 } = 2.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.2 }{ 2 * sin 35° } = 8.89 ; ;




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