14 16 16 triangle

Acute isosceles triangle.

Sides: a = 14   b = 16   c = 16

Area: T = 100.712246199
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 51.88989595447° = 51°53'20″ = 0.90656331895 rad
Angle ∠ B = β = 64.05655202276° = 64°3'20″ = 1.1187979732 rad
Angle ∠ C = γ = 64.05655202276° = 64°3'20″ = 1.1187979732 rad

Height: ha = 14.38774945699
Height: hb = 12.58990577487
Height: hc = 12.58990577487

Median: ma = 14.38774945699
Median: mb = 12.72879220614
Median: mc = 12.72879220614

Inradius: r = 4.37988026952
Circumradius: R = 8.89766149998

Vertex coordinates: A[16; 0] B[0; 0] C[6.125; 12.58990577487]
Centroid: CG[7.375; 4.19663525829]
Coordinates of the circumscribed circle: U[8; 3.89222690624]
Coordinates of the inscribed circle: I[7; 4.37988026952]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.1111040455° = 128°6'40″ = 0.90656331895 rad
∠ B' = β' = 115.9444479772° = 115°56'40″ = 1.1187979732 rad
∠ C' = γ' = 115.9444479772° = 115°56'40″ = 1.1187979732 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 = 16 ; ; c = 16 ; ;

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

p = a+b+c = 14+16+16 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-14)(23-16)(23-16) } ; ; T = sqrt{ 10143 } = 100.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 100.71 }{ 14 } = 14.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 100.71 }{ 16 } = 12.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 100.71 }{ 16 } = 12.59 ; ;

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**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 51° 53'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 64° 3'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-14**2-16**2 }{ 2 * 16 * 14 } ) = 64° 3'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 100.71 }{ 23 } = 4.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 51° 53'20" } = 8.9 ; ;




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