14 14 16 triangle

Acute isosceles triangle.

Sides: a = 14   b = 14   c = 16

Area: T = 91.91330023446
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 55.1550095421° = 55°9' = 0.96325507479 rad
Angle ∠ B = β = 55.1550095421° = 55°9' = 0.96325507479 rad
Angle ∠ C = γ = 69.76998091581° = 69°41'59″ = 1.21664911578 rad

Height: ha = 13.13304289064
Height: hb = 13.13304289064
Height: hc = 11.48991252931

Median: ma = 13.30441346957
Median: mb = 13.30441346957
Median: mc = 11.48991252931

Inradius: r = 4.17878637429
Circumradius: R = 8.53298051418

Vertex coordinates: A[16; 0] B[0; 0] C[8; 11.48991252931]
Centroid: CG[8; 3.8329708431]
Coordinates of the circumscribed circle: U[8; 2.95993201512]
Coordinates of the inscribed circle: I[8; 4.17878637429]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.8549904579° = 124°51' = 0.96325507479 rad
∠ B' = β' = 124.8549904579° = 124°51' = 0.96325507479 rad
∠ C' = γ' = 110.3300190842° = 110°18'1″ = 1.21664911578 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 = 16 ; ;

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

p = a+b+c = 14+14+16 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-14)(22-14)(22-16) } ; ; T = sqrt{ 8448 } = 91.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.91 }{ 14 } = 13.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.91 }{ 14 } = 13.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.91 }{ 16 } = 11.49 ; ;

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**2-16**2 }{ 2 * 14 * 16 } ) = 55° 9' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 55° 9' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 69° 41'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.91 }{ 22 } = 4.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 55° 9' } = 8.53 ; ;




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