5 13 13 triangle

Acute isosceles triangle.

Sides: a = 5   b = 13   c = 13

Area: T = 31.89333770554
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 22.17549784219° = 22°10'30″ = 0.3877026385 rad
Angle ∠ B = β = 78.9132510789° = 78°54'45″ = 1.37772831343 rad
Angle ∠ C = γ = 78.9132510789° = 78°54'45″ = 1.37772831343 rad

Height: ha = 12.75773508222
Height: hb = 4.90766733931
Height: hc = 4.90766733931

Median: ma = 12.75773508222
Median: mb = 7.39993242935
Median: mc = 7.39993242935

Inradius: r = 2.05876372294
Circumradius: R = 6.62436322241

Vertex coordinates: A[13; 0] B[0; 0] C[0.96215384615; 4.90766733931]
Centroid: CG[4.65438461538; 1.63655577977]
Coordinates of the circumscribed circle: U[6.5; 1.27437754277]
Coordinates of the inscribed circle: I[2.5; 2.05876372294]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.8255021578° = 157°49'30″ = 0.3877026385 rad
∠ B' = β' = 101.0877489211° = 101°5'15″ = 1.37772831343 rad
∠ C' = γ' = 101.0877489211° = 101°5'15″ = 1.37772831343 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 = 5 ; ; b = 13 ; ; c = 13 ; ;

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

p = a+b+c = 5+13+13 = 31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31 }{ 2 } = 15.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.5 * (15.5-5)(15.5-13)(15.5-13) } ; ; T = sqrt{ 1017.19 } = 31.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.89 }{ 5 } = 12.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.89 }{ 13 } = 4.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.89 }{ 13 } = 4.91 ; ;

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{ 5**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 22° 10'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-5**2-13**2 }{ 2 * 5 * 13 } ) = 78° 54'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-5**2-13**2 }{ 2 * 13 * 5 } ) = 78° 54'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.89 }{ 15.5 } = 2.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 22° 10'30" } = 6.62 ; ;




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