Triangle calculator

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

You have entered height hc, angle α, angle β and angle γ.

Acute isosceles triangle.

Sides: a = 55.16988959481   b = 55.16988959481   c = 46.63107658155

Area: T = 1165.769914539
Perimeter: p = 156.9698557712
Semiperimeter: s = 78.48442788559

Angle ∠ A = α = 65° = 1.13444640138 rad
Angle ∠ B = β = 65° = 1.13444640138 rad
Angle ∠ C = γ = 50° = 0.8732664626 rad

Height: ha = 42.26218261741
Height: hb = 42.26218261741
Height: hc = 50

Median: ma = 42.99897188907
Median: mb = 42.99897188907
Median: mc = 50

Inradius: r = 14.85435370699
Circumradius: R = 30.43660708014

Vertex coordinates: A[46.63107658155; 0] B[0; 0] C[23.31553829077; 50]
Centroid: CG[23.31553829077; 16.66766666667]
Coordinates of the circumscribed circle: U[23.31553829077; 19.56439291987]
Coordinates of the inscribed circle: I[23.31553829077; 14.85435370699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115° = 1.13444640138 rad
∠ B' = β' = 115° = 1.13444640138 rad
∠ C' = γ' = 130° = 0.8732664626 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 = 55.17 ; ; b = 55.17 ; ; c = 46.63 ; ;

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

p = a+b+c = 55.17+55.17+46.63 = 156.97 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 156.97 }{ 2 } = 78.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 78.48 * (78.48-55.17)(78.48-55.17)(78.48-46.63) } ; ; T = sqrt{ 1359017.7 } = 1165.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1165.77 }{ 55.17 } = 42.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1165.77 }{ 55.17 } = 42.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1165.77 }{ 46.63 } = 50 ; ;

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{ 55.17**2-55.17**2-46.63**2 }{ 2 * 55.17 * 46.63 } ) = 65° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 55.17**2-55.17**2-46.63**2 }{ 2 * 55.17 * 46.63 } ) = 65° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 46.63**2-55.17**2-55.17**2 }{ 2 * 55.17 * 55.17 } ) = 50° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1165.77 }{ 78.48 } = 14.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 55.17 }{ 2 * sin 65° } = 30.44 ; ;




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