14 14 27 triangle

Obtuse isosceles triangle.

Sides: a = 14   b = 14   c = 27

Area: T = 50.05993397879
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 15.35988855808° = 15°21'32″ = 0.26880631228 rad
Angle ∠ B = β = 15.35988855808° = 15°21'32″ = 0.26880631228 rad
Angle ∠ C = γ = 149.2822228838° = 149°16'56″ = 2.60554664079 rad

Height: ha = 7.15113342554
Height: hb = 7.15113342554
Height: hc = 3.70880992435

Median: ma = 20.33546994077
Median: mb = 20.33546994077
Median: mc = 3.70880992435

Inradius: r = 1.82203396287
Circumradius: R = 26.42986346086

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 3.70880992435]
Centroid: CG[13.5; 1.23660330812]
Coordinates of the circumscribed circle: U[13.5; -22.7210535365]
Coordinates of the inscribed circle: I[13.5; 1.82203396287]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6411114419° = 164°38'28″ = 0.26880631228 rad
∠ B' = β' = 164.6411114419° = 164°38'28″ = 0.26880631228 rad
∠ C' = γ' = 30.71877711616° = 30°43'4″ = 2.60554664079 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 = 14 ; ; c = 27 ; ;

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

p = a+b+c = 14+14+27 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-14)(27.5-14)(27.5-27) } ; ; T = sqrt{ 2505.94 } = 50.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.06 }{ 14 } = 7.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.06 }{ 14 } = 7.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.06 }{ 27 } = 3.71 ; ;

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**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 15° 21'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 15° 21'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 149° 16'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.06 }{ 27.5 } = 1.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 15° 21'32" } = 26.43 ; ;




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