4 14 14 triangle

Acute isosceles triangle.

Sides: a = 4   b = 14   c = 14

Area: T = 27.71328129211
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 16.42664214035° = 16°25'35″ = 0.28766951378 rad
Angle ∠ B = β = 81.78767892983° = 81°47'12″ = 1.42774487579 rad
Angle ∠ C = γ = 81.78767892983° = 81°47'12″ = 1.42774487579 rad

Height: ha = 13.85664064606
Height: hb = 3.95989732744
Height: hc = 3.95989732744

Median: ma = 13.85664064606
Median: mb = 7.55498344353
Median: mc = 7.55498344353

Inradius: r = 1.73220508076
Circumradius: R = 7.07325407976

Vertex coordinates: A[14; 0] B[0; 0] C[0.57114285714; 3.95989732744]
Centroid: CG[4.85771428571; 1.32196577581]
Coordinates of the circumscribed circle: U[7; 1.01103629711]
Coordinates of the inscribed circle: I[2; 1.73220508076]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.5743578597° = 163°34'25″ = 0.28766951378 rad
∠ B' = β' = 98.21332107017° = 98°12'48″ = 1.42774487579 rad
∠ C' = γ' = 98.21332107017° = 98°12'48″ = 1.42774487579 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 = 14 ; ; c = 14 ; ;

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

p = a+b+c = 4+14+14 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-4)(16-14)(16-14) } ; ; T = sqrt{ 768 } = 27.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.71 }{ 4 } = 13.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.71 }{ 14 } = 3.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.71 }{ 14 } = 3.96 ; ;

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**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 16° 25'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-4**2-14**2 }{ 2 * 4 * 14 } ) = 81° 47'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-4**2-14**2 }{ 2 * 14 * 4 } ) = 81° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.71 }{ 16 } = 1.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 16° 25'35" } = 7.07 ; ;




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