Triangle calculator

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

You have entered side b, angle β and angle γ.

Acute scalene triangle.

Sides: a = 0.2577432919   b = 0.3   c = 0.32994556414

Area: T = 0.03767249883
Perimeter: p = 0.88768885604
Semiperimeter: s = 0.44334442802

Angle ∠ A = α = 48° = 0.8387758041 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 72° = 1.25766370614 rad

Height: ha = 0.28553169549
Height: hb = 0.24548332551
Height: hc = 0.22329434476

Median: ma = 0.28875805676
Median: mb = 0.25547672737
Median: mc = 0.2265833122

Inradius: r = 0.08328175938
Circumradius: R = 0.17332050808

Vertex coordinates: A[0.32994556414; 0] B[0; 0] C[0.12987164595; 0.22329434476]
Centroid: CG[0.15327240336; 0.07443144825]
Coordinates of the circumscribed circle: U[0.16547278207; 0.05435233135]
Coordinates of the inscribed circle: I[0.14334442802; 0.08328175938]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132° = 0.8387758041 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 108° = 1.25766370614 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 = 0.26 ; ; b = 0.3 ; ; c = 0.33 ; ;

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

p = a+b+c = 0.26+0.3+0.33 = 0.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.89 }{ 2 } = 0.44 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.44 * (0.44-0.26)(0.44-0.3)(0.44-0.33) } ; ; T = sqrt{ 0 } = 0.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.04 }{ 0.26 } = 0.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.04 }{ 0.3 } = 0.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.04 }{ 0.33 } = 0.22 ; ;

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{ 0.26**2-0.3**2-0.33**2 }{ 2 * 0.3 * 0.33 } ) = 48° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.3**2-0.26**2-0.33**2 }{ 2 * 0.26 * 0.33 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.33**2-0.26**2-0.3**2 }{ 2 * 0.3 * 0.26 } ) = 72° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.04 }{ 0.44 } = 0.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.26 }{ 2 * sin 48° } = 0.17 ; ;




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