6 13 13 triangle

Acute isosceles triangle.

Sides: a = 6   b = 13   c = 13

Area: T = 37.9477331922
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 26.68547275942° = 26°41'5″ = 0.46657363565 rad
Angle ∠ B = β = 76.65876362029° = 76°39'28″ = 1.33879281485 rad
Angle ∠ C = γ = 76.65876362029° = 76°39'28″ = 1.33879281485 rad

Height: ha = 12.64991106407
Height: hb = 5.83880510649
Height: hc = 5.83880510649

Median: ma = 12.64991106407
Median: mb = 7.76220873481
Median: mc = 7.76220873481

Inradius: r = 2.37217082451
Circumradius: R = 6.68803115571

Vertex coordinates: A[13; 0] B[0; 0] C[1.38546153846; 5.83880510649]
Centroid: CG[4.79548717949; 1.94660170216]
Coordinates of the circumscribed circle: U[6.5; 1.54216103593]
Coordinates of the inscribed circle: I[3; 2.37217082451]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.3155272406° = 153°18'55″ = 0.46657363565 rad
∠ B' = β' = 103.3422363797° = 103°20'32″ = 1.33879281485 rad
∠ C' = γ' = 103.3422363797° = 103°20'32″ = 1.33879281485 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 = 6 ; ; b = 13 ; ; c = 13 ; ;

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

p = a+b+c = 6+13+13 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-6)(16-13)(16-13) } ; ; T = sqrt{ 1440 } = 37.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.95 }{ 6 } = 12.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.95 }{ 13 } = 5.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.95 }{ 13 } = 5.84 ; ;

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{ 6**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 26° 41'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-6**2-13**2 }{ 2 * 6 * 13 } ) = 76° 39'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-6**2-13**2 }{ 2 * 13 * 6 } ) = 76° 39'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.95 }{ 16 } = 2.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 26° 41'5" } = 6.68 ; ;




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