12 14 14 triangle

Acute isosceles triangle.

Sides: a = 12   b = 14   c = 14

Area: T = 75.8954663844
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 50.75438670503° = 50°45'14″ = 0.88658220881 rad
Angle ∠ B = β = 64.62330664748° = 64°37'23″ = 1.12878852827 rad
Angle ∠ C = γ = 64.62330664748° = 64°37'23″ = 1.12878852827 rad

Height: ha = 12.64991106407
Height: hb = 10.84220948349
Height: hc = 10.84220948349

Median: ma = 12.64991106407
Median: mb = 11
Median: mc = 11

Inradius: r = 3.79547331922
Circumradius: R = 7.74875802674

Vertex coordinates: A[14; 0] B[0; 0] C[5.14328571429; 10.84220948349]
Centroid: CG[6.3810952381; 3.61440316116]
Coordinates of the circumscribed circle: U[7; 3.32203915432]
Coordinates of the inscribed circle: I[6; 3.79547331922]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.246613295° = 129°14'46″ = 0.88658220881 rad
∠ B' = β' = 115.3776933525° = 115°22'37″ = 1.12878852827 rad
∠ C' = γ' = 115.3776933525° = 115°22'37″ = 1.12878852827 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 = 12 ; ; b = 14 ; ; c = 14 ; ;

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

p = a+b+c = 12+14+14 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-12)(20-14)(20-14) } ; ; T = sqrt{ 5760 } = 75.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75.89 }{ 12 } = 12.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75.89 }{ 14 } = 10.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75.89 }{ 14 } = 10.84 ; ;

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{ 12**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 50° 45'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-12**2-14**2 }{ 2 * 12 * 14 } ) = 64° 37'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-12**2-14**2 }{ 2 * 14 * 12 } ) = 64° 37'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75.89 }{ 20 } = 3.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 50° 45'14" } = 7.75 ; ;




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