Triangle calculator

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

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

Acute isosceles triangle.

Sides: a = 17.32105080757   b = 17.32105080757   c = 17.32105080757

Area: T = 129.9043810568
Perimeter: p = 51.96215242271
Semiperimeter: s = 25.98107621135

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 15
Height: hb = 15
Height: hc = 15

Median: ma = 15
Median: mb = 15
Median: mc = 15

Inradius: r = 5
Circumradius: R = 10

Vertex coordinates: A[17.32105080757; 0] B[0; 0] C[8.66602540378; 15]
Centroid: CG[8.66602540378; 5]
Coordinates of the circumscribed circle: U[8.66602540378; 5]
Coordinates of the inscribed circle: I[8.66602540378; 5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 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 = 17.32 ; ; b = 17.32 ; ; c = 17.32 ; ;

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

p = a+b+c = 17.32+17.32+17.32 = 51.96 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51.96 }{ 2 } = 25.98 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.98 * (25.98-17.32)(25.98-17.32)(25.98-17.32) } ; ; T = sqrt{ 16875 } = 129.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 129.9 }{ 17.32 } = 15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 129.9 }{ 17.32 } = 15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 129.9 }{ 17.32 } = 15 ; ;

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{ 17.32**2-17.32**2-17.32**2 }{ 2 * 17.32 * 17.32 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17.32**2-17.32**2-17.32**2 }{ 2 * 17.32 * 17.32 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17.32**2-17.32**2-17.32**2 }{ 2 * 17.32 * 17.32 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 129.9 }{ 25.98 } = 5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.32 }{ 2 * sin 60° } = 10 ; ;




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