8 13 13 triangle

Acute isosceles triangle.

Sides: a = 8   b = 13   c = 13

Area: T = 49.47772675074
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 35.84404262788° = 35°50'26″ = 0.62655334439 rad
Angle ∠ B = β = 72.08797868606° = 72°4'47″ = 1.25880296049 rad
Angle ∠ C = γ = 72.08797868606° = 72°4'47″ = 1.25880296049 rad

Height: ha = 12.36993168769
Height: hb = 7.61218873088
Height: hc = 7.61218873088

Median: ma = 12.36993168769
Median: mb = 8.61768439698
Median: mc = 8.61768439698

Inradius: r = 2.91104275004
Circumradius: R = 6.83114201052

Vertex coordinates: A[13; 0] B[0; 0] C[2.46215384615; 7.61218873088]
Centroid: CG[5.15438461538; 2.53772957696]
Coordinates of the circumscribed circle: U[6.5; 2.1021975417]
Coordinates of the inscribed circle: I[4; 2.91104275004]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.1659573721° = 144°9'34″ = 0.62655334439 rad
∠ B' = β' = 107.9220213139° = 107°55'13″ = 1.25880296049 rad
∠ C' = γ' = 107.9220213139° = 107°55'13″ = 1.25880296049 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 = 8 ; ; b = 13 ; ; c = 13 ; ;

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

p = a+b+c = 8+13+13 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-8)(17-13)(17-13) } ; ; T = sqrt{ 2448 } = 49.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.48 }{ 8 } = 12.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.48 }{ 13 } = 7.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.48 }{ 13 } = 7.61 ; ;

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{ 8**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 35° 50'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-8**2-13**2 }{ 2 * 8 * 13 } ) = 72° 4'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-8**2-13**2 }{ 2 * 13 * 8 } ) = 72° 4'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.48 }{ 17 } = 2.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 35° 50'26" } = 6.83 ; ;




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