1 30 30 triangle

Acute isosceles triangle.

Sides: a = 1   b = 30   c = 30

Area: T = 14.9987916522
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 1.91099477476° = 1°54'36″ = 0.03333348767 rad
Angle ∠ B = β = 89.04550261262° = 89°2'42″ = 1.55441288884 rad
Angle ∠ C = γ = 89.04550261262° = 89°2'42″ = 1.55441288884 rad

Height: ha = 29.99658330439
Height: hb = 10.9998611015
Height: hc = 10.9998611015

Median: ma = 29.99658330439
Median: mb = 15.01766574177
Median: mc = 15.01766574177

Inradius: r = 0.49217349679
Circumradius: R = 15.00220837675

Vertex coordinates: A[30; 0] B[0; 0] C[0.01766666667; 10.9998611015]
Centroid: CG[10.00655555556; 0.33332870338]
Coordinates of the circumscribed circle: U[15; 0.25500347295]
Coordinates of the inscribed circle: I[0.5; 0.49217349679]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178.0990052252° = 178°5'24″ = 0.03333348767 rad
∠ B' = β' = 90.95549738738° = 90°57'18″ = 1.55441288884 rad
∠ C' = γ' = 90.95549738738° = 90°57'18″ = 1.55441288884 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 = 1 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 1+30+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-1)(30.5-30)(30.5-30) } ; ; T = sqrt{ 224.94 } = 15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15 }{ 1 } = 30 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15 }{ 30 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15 }{ 30 } = 1 ; ;

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{ 1**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 1° 54'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-1**2-30**2 }{ 2 * 1 * 30 } ) = 89° 2'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-1**2-30**2 }{ 2 * 30 * 1 } ) = 89° 2'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15 }{ 30.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 1° 54'36" } = 15 ; ;




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