Equilateral triangle calculator (h)

Please enter one property of the equilateral triangle

Use symbols: a, h, T, p, r, R


You have entered height h.

Equilateral triangle.

Sides: a = 8.08329037687   b = 8.08329037687   c = 8.08329037687

Area: T = 28.29901631903
Perimeter: p = 24.2498711306
Semiperimeter: s = 12.1244355653

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

Height: ha = 7
Height: hb = 7
Height: hc = 7

Median: ma = 7
Median: mb = 7
Median: mc = 7

Inradius: r = 2.33333333333
Circumradius: R = 4.66766666667

Vertex coordinates: A[8.08329037687; 0] B[0; 0] C[4.04114518843; 7]
Centroid: CG[4.04114518843; 2.33333333333]
Coordinates of the circumscribed circle: U[4.04114518843; 2.33333333333]
Coordinates of the inscribed circle: I[4.04114518843; 2.33333333333]

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?

1. Input data entered: height h

hc = 7 ; ;

2. From we calculate side a - Pythagorean theorem:

a = 2h / sqrt{ 3 } = 2 * 7 / sqrt{ 3 } = 8.083 ; ;

3. From side a we calculate b,c:

b = c = a = 8.083 ; ;


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 = 8.08 ; ; b = 8.08 ; ; c = 8.08 ; ;

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

p = a+b+c = 8.08+8.08+8.08 = 24.25 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.25 }{ 2 } = 12.12 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.12 * (12.12-8.08)(12.12-8.08)(12.12-8.08) } ; ; T = sqrt{ 800.33 } = 28.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 28.29 }{ 8.08 } = 7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 28.29 }{ 8.08 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 28.29 }{ 8.08 } = 7 ; ;

8. 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{ 8.08**2-8.08**2-8.08**2 }{ 2 * 8.08 * 8.08 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.08**2-8.08**2-8.08**2 }{ 2 * 8.08 * 8.08 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.08**2-8.08**2-8.08**2 }{ 2 * 8.08 * 8.08 } ) = 60° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 28.29 }{ 12.12 } = 2.33 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.08 }{ 2 * sin 60° } = 4.67 ; ;




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