3 30 30 triangle

Acute isosceles triangle.

Sides: a = 3   b = 30   c = 30

Area: T = 44.94437147997
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 5.73219679652° = 5°43'55″ = 0.11000417136 rad
Angle ∠ B = β = 87.13440160174° = 87°8'2″ = 1.521077547 rad
Angle ∠ C = γ = 87.13440160174° = 87°8'2″ = 1.521077547 rad

Height: ha = 29.96224765332
Height: hb = 2.99662476533
Height: hc = 2.99662476533

Median: ma = 29.96224765332
Median: mb = 15.14992574075
Median: mc = 15.14992574075

Inradius: r = 1.42767845968
Circumradius: R = 15.01987852297

Vertex coordinates: A[30; 0] B[0; 0] C[0.15; 2.99662476533]
Centroid: CG[10.05; 0.99987492178]
Coordinates of the circumscribed circle: U[15; 0.75109392615]
Coordinates of the inscribed circle: I[1.5; 1.42767845968]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.2688032035° = 174°16'5″ = 0.11000417136 rad
∠ B' = β' = 92.86659839826° = 92°51'58″ = 1.521077547 rad
∠ C' = γ' = 92.86659839826° = 92°51'58″ = 1.521077547 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 = 3 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 3+30+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-3)(31.5-30)(31.5-30) } ; ; T = sqrt{ 2019.94 } = 44.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.94 }{ 3 } = 29.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.94 }{ 30 } = 3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.94 }{ 30 } = 3 ; ;

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{ 3**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 5° 43'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-3**2-30**2 }{ 2 * 3 * 30 } ) = 87° 8'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-3**2-30**2 }{ 2 * 30 * 3 } ) = 87° 8'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.94 }{ 31.5 } = 1.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 5° 43'55" } = 15.02 ; ;




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