3 14 14 triangle

Acute isosceles triangle.

Sides: a = 3   b = 14   c = 14

Area: T = 20.87991163606
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 12.30112796559° = 12°18'5″ = 0.21546978322 rad
Angle ∠ B = β = 83.84993601721° = 83°50'58″ = 1.46334474107 rad
Angle ∠ C = γ = 83.84993601721° = 83°50'58″ = 1.46334474107 rad

Height: ha = 13.91994109071
Height: hb = 2.98327309087
Height: hc = 2.98327309087

Median: ma = 13.91994109071
Median: mb = 7.31443694192
Median: mc = 7.31443694192

Inradius: r = 1.34770397652
Circumradius: R = 7.04105278394

Vertex coordinates: A[14; 0] B[0; 0] C[0.32114285714; 2.98327309087]
Centroid: CG[4.77438095238; 0.99442436362]
Coordinates of the circumscribed circle: U[7; 0.75443422685]
Coordinates of the inscribed circle: I[1.5; 1.34770397652]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.6998720344° = 167°41'55″ = 0.21546978322 rad
∠ B' = β' = 96.15106398279° = 96°9'2″ = 1.46334474107 rad
∠ C' = γ' = 96.15106398279° = 96°9'2″ = 1.46334474107 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 = 3 ; ; b = 14 ; ; c = 14 ; ;

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

p = a+b+c = 3+14+14 = 31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31 }{ 2 } = 15.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.5 * (15.5-3)(15.5-14)(15.5-14) } ; ; T = sqrt{ 435.94 } = 20.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.88 }{ 3 } = 13.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.88 }{ 14 } = 2.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.88 }{ 14 } = 2.98 ; ;

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{ 3**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 12° 18'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-3**2-14**2 }{ 2 * 3 * 14 } ) = 83° 50'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-3**2-14**2 }{ 2 * 14 * 3 } ) = 83° 50'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.88 }{ 15.5 } = 1.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 12° 18'5" } = 7.04 ; ;




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