14 30 30 triangle

Acute isosceles triangle.

Sides: a = 14   b = 30   c = 30

Area: T = 204.2033330041
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 26.98767976431° = 26°59'12″ = 0.47110084734 rad
Angle ∠ B = β = 76.50766011784° = 76°30'24″ = 1.33552920901 rad
Angle ∠ C = γ = 76.50766011784° = 76°30'24″ = 1.33552920901 rad

Height: ha = 29.17219042916
Height: hb = 13.61435553361
Height: hc = 13.61435553361

Median: ma = 29.17219042916
Median: mb = 17.97222007556
Median: mc = 17.97222007556

Inradius: r = 5.519900892
Circumradius: R = 15.42658013293

Vertex coordinates: A[30; 0] B[0; 0] C[3.26766666667; 13.61435553361]
Centroid: CG[11.08988888889; 4.53878517787]
Coordinates of the circumscribed circle: U[15; 3.59993536435]
Coordinates of the inscribed circle: I[7; 5.519900892]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.0133202357° = 153°48″ = 0.47110084734 rad
∠ B' = β' = 103.4933398822° = 103°29'36″ = 1.33552920901 rad
∠ C' = γ' = 103.4933398822° = 103°29'36″ = 1.33552920901 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 = 14 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 14+30+30 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-14)(37-30)(37-30) } ; ; T = sqrt{ 41699 } = 204.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 204.2 }{ 14 } = 29.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 204.2 }{ 30 } = 13.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 204.2 }{ 30 } = 13.61 ; ;

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{ 14**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 26° 59'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 76° 30'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-30**2 }{ 2 * 30 * 14 } ) = 76° 30'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 204.2 }{ 37 } = 5.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 26° 59'12" } = 15.43 ; ;




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