4 30 30 triangle

Acute isosceles triangle.

Sides: a = 4   b = 30   c = 30

Area: T = 59.86765181884
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 7.64551074586° = 7°38'42″ = 0.13334322968 rad
Angle ∠ B = β = 86.17774462707° = 86°10'39″ = 1.50440801784 rad
Angle ∠ C = γ = 86.17774462707° = 86°10'39″ = 1.50440801784 rad

Height: ha = 29.93332590942
Height: hb = 3.99111012126
Height: hc = 3.99111012126

Median: ma = 29.93332590942
Median: mb = 15.26443375225
Median: mc = 15.26443375225

Inradius: r = 1.87108286934
Circumradius: R = 15.03334448576

Vertex coordinates: A[30; 0] B[0; 0] C[0.26766666667; 3.99111012126]
Centroid: CG[10.08988888889; 1.33303670709]
Coordinates of the circumscribed circle: U[15; 1.00222296572]
Coordinates of the inscribed circle: I[2; 1.87108286934]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.3554892541° = 172°21'18″ = 0.13334322968 rad
∠ B' = β' = 93.82325537293° = 93°49'21″ = 1.50440801784 rad
∠ C' = γ' = 93.82325537293° = 93°49'21″ = 1.50440801784 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 = 4 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 4+30+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-4)(32-30)(32-30) } ; ; T = sqrt{ 3584 } = 59.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.87 }{ 4 } = 29.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.87 }{ 30 } = 3.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.87 }{ 30 } = 3.99 ; ;

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{ 4**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 7° 38'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-4**2-30**2 }{ 2 * 4 * 30 } ) = 86° 10'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-4**2-30**2 }{ 2 * 30 * 4 } ) = 86° 10'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.87 }{ 32 } = 1.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 7° 38'42" } = 15.03 ; ;




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