1 13 13 triangle

Acute isosceles triangle.

Sides: a = 1   b = 13   c = 13

Area: T = 6.49551905284
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 4.40884550079° = 4°24'30″ = 0.07769420548 rad
Angle ∠ B = β = 87.7965772496° = 87°47'45″ = 1.53223252994 rad
Angle ∠ C = γ = 87.7965772496° = 87°47'45″ = 1.53223252994 rad

Height: ha = 12.99903810568
Height: hb = 0.99992600813
Height: hc = 0.99992600813

Median: ma = 12.99903810568
Median: mb = 6.53883484153
Median: mc = 6.53883484153

Inradius: r = 0.48111252243
Circumradius: R = 6.50548130329

Vertex coordinates: A[13; 0] B[0; 0] C[0.03884615385; 0.99992600813]
Centroid: CG[4.34661538462; 0.33330866938]
Coordinates of the circumscribed circle: U[6.5; 0.25501851166]
Coordinates of the inscribed circle: I[0.5; 0.48111252243]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5921544992° = 175°35'30″ = 0.07769420548 rad
∠ B' = β' = 92.2044227504° = 92°12'15″ = 1.53223252994 rad
∠ C' = γ' = 92.2044227504° = 92°12'15″ = 1.53223252994 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 = 1 ; ; b = 13 ; ; c = 13 ; ;

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

p = a+b+c = 1+13+13 = 27 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27 }{ 2 } = 13.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.5 * (13.5-1)(13.5-13)(13.5-13) } ; ; T = sqrt{ 42.19 } = 6.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.5 }{ 1 } = 12.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.5 }{ 13 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.5 }{ 13 } = 1 ; ;

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{ 1**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 4° 24'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-1**2-13**2 }{ 2 * 1 * 13 } ) = 87° 47'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-1**2-13**2 }{ 2 * 13 * 1 } ) = 87° 47'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.5 }{ 13.5 } = 0.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 4° 24'30" } = 6.5 ; ;




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