3 13 13 triangle

Acute isosceles triangle.

Sides: a = 3   b = 13   c = 13

Area: T = 19.37697573552
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 13.25216191296° = 13°15'6″ = 0.2311284385 rad
Angle ∠ B = β = 83.37441904352° = 83°22'27″ = 1.45551541343 rad
Angle ∠ C = γ = 83.37441904352° = 83°22'27″ = 1.45551541343 rad

Height: ha = 12.91331715701
Height: hb = 2.987996267
Height: hc = 2.987996267

Median: ma = 12.91331715701
Median: mb = 6.83773971656
Median: mc = 6.83773971656

Inradius: r = 1.33658453348
Circumradius: R = 6.5443706133

Vertex coordinates: A[13; 0] B[0; 0] C[0.34661538462; 2.987996267]
Centroid: CG[4.44987179487; 0.993332089]
Coordinates of the circumscribed circle: U[6.5; 0.75550430153]
Coordinates of the inscribed circle: I[1.5; 1.33658453348]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.748838087° = 166°44'54″ = 0.2311284385 rad
∠ B' = β' = 96.62658095648° = 96°37'33″ = 1.45551541343 rad
∠ C' = γ' = 96.62658095648° = 96°37'33″ = 1.45551541343 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 = 3 ; ; b = 13 ; ; c = 13 ; ;

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

p = a+b+c = 3+13+13 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-3)(14.5-13)(14.5-13) } ; ; T = sqrt{ 375.19 } = 19.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.37 }{ 3 } = 12.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.37 }{ 13 } = 2.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.37 }{ 13 } = 2.98 ; ;

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{ 3**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 13° 15'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-3**2-13**2 }{ 2 * 3 * 13 } ) = 83° 22'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-3**2-13**2 }{ 2 * 13 * 3 } ) = 83° 22'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.37 }{ 14.5 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 13° 15'6" } = 6.54 ; ;




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