6 30 30 triangle

Acute isosceles triangle.

Sides: a = 6   b = 30   c = 30

Area: T = 89.54988693396
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 11.47883409545° = 11°28'42″ = 0.22003348423 rad
Angle ∠ B = β = 84.26108295227° = 84°15'39″ = 1.47106289056 rad
Angle ∠ C = γ = 84.26108295227° = 84°15'39″ = 1.47106289056 rad

Height: ha = 29.85496231132
Height: hb = 5.97699246226
Height: hc = 5.97699246226

Median: ma = 29.85496231132
Median: mb = 15.58884572681
Median: mc = 15.58884572681

Inradius: r = 2.71436021012
Circumradius: R = 15.07655672289

Vertex coordinates: A[30; 0] B[0; 0] C[0.6; 5.97699246226]
Centroid: CG[10.2; 1.99899748742]
Coordinates of the circumscribed circle: U[15; 1.50875567229]
Coordinates of the inscribed circle: I[3; 2.71436021012]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5221659045° = 168°31'18″ = 0.22003348423 rad
∠ B' = β' = 95.73991704773° = 95°44'21″ = 1.47106289056 rad
∠ C' = γ' = 95.73991704773° = 95°44'21″ = 1.47106289056 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 = 6 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 6+30+30 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-6)(33-30)(33-30) } ; ; T = sqrt{ 8019 } = 89.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 89.55 }{ 6 } = 29.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 89.55 }{ 30 } = 5.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 89.55 }{ 30 } = 5.97 ; ;

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{ 6**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 11° 28'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-6**2-30**2 }{ 2 * 6 * 30 } ) = 84° 15'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-6**2-30**2 }{ 2 * 30 * 6 } ) = 84° 15'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 89.55 }{ 33 } = 2.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 28'42" } = 15.08 ; ;




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