13 28 28 triangle

Acute isosceles triangle.

Sides: a = 13   b = 28   c = 28

Area: T = 177.0288069808
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 26.84765272069° = 26°50'48″ = 0.46985602925 rad
Angle ∠ B = β = 76.57767363965° = 76°34'36″ = 1.33765161806 rad
Angle ∠ C = γ = 76.57767363965° = 76°34'36″ = 1.33765161806 rad

Height: ha = 27.23550876628
Height: hb = 12.64548621292
Height: hc = 12.64548621292

Median: ma = 27.23550876628
Median: mb = 16.74881342244
Median: mc = 16.74881342244

Inradius: r = 5.13112484002
Circumradius: R = 14.39331976593

Vertex coordinates: A[28; 0] B[0; 0] C[3.01878571429; 12.64548621292]
Centroid: CG[10.33992857143; 4.21549540431]
Coordinates of the circumscribed circle: U[14; 3.34112780281]
Coordinates of the inscribed circle: I[6.5; 5.13112484002]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.1533472793° = 153°9'12″ = 0.46985602925 rad
∠ B' = β' = 103.4233263603° = 103°25'24″ = 1.33765161806 rad
∠ C' = γ' = 103.4233263603° = 103°25'24″ = 1.33765161806 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 = 13 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 13+28+28 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-13)(34.5-28)(34.5-28) } ; ; T = sqrt{ 31338.94 } = 177.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 177.03 }{ 13 } = 27.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 177.03 }{ 28 } = 12.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 177.03 }{ 28 } = 12.64 ; ;

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{ 13**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 26° 50'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-13**2-28**2 }{ 2 * 13 * 28 } ) = 76° 34'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-13**2-28**2 }{ 2 * 28 * 13 } ) = 76° 34'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 177.03 }{ 34.5 } = 5.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 26° 50'48" } = 14.39 ; ;




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