Triangle calculator

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

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

Right scalene triangle.

Sides: a = 34   b = 19.63299091524   c = 39.26598183049

Area: T = 333.7088455592
Perimeter: p = 92.89897274573
Semiperimeter: s = 46.44548637287

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 19.63299091524
Height: hb = 34
Height: hc = 17

Median: ma = 25.96879289381
Median: mb = 35.38883219909
Median: mc = 19.63299091524

Inradius: r = 7.18550454238
Circumradius: R = 19.63299091524

Vertex coordinates: A[39.26598183049; 0] B[0; 0] C[29.44548637287; 17]
Centroid: CG[22.90215606779; 5.66766666667]
Coordinates of the circumscribed circle: U[19.63299091524; 0]
Coordinates of the inscribed circle: I[26.81549545762; 7.18550454238]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 34 ; ; b = 19.63 ; ; c = 39.26 ; ;

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

p = a+b+c = 34+19.63+39.26 = 92.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 92.89 }{ 2 } = 46.44 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 46.44 * (46.44-34)(46.44-19.63)(46.44-39.26) } ; ; T = sqrt{ 111361.33 } = 333.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 333.71 }{ 34 } = 19.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 333.71 }{ 19.63 } = 34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 333.71 }{ 39.26 } = 17 ; ;

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{ 34**2-19.63**2-39.26**2 }{ 2 * 19.63 * 39.26 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19.63**2-34**2-39.26**2 }{ 2 * 34 * 39.26 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 39.26**2-34**2-19.63**2 }{ 2 * 19.63 * 34 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 333.71 }{ 46.44 } = 7.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 34 }{ 2 * sin 60° } = 19.63 ; ;




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