13 13 20 triangle

Obtuse isosceles triangle.

Sides: a = 13   b = 13   c = 20

Area: T = 83.06662386292
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 39.71551372318° = 39°42'55″ = 0.69331599076 rad
Angle ∠ B = β = 39.71551372318° = 39°42'55″ = 0.69331599076 rad
Angle ∠ C = γ = 100.5769725536° = 100°34'11″ = 1.75552728384 rad

Height: ha = 12.77994213276
Height: hb = 12.77994213276
Height: hc = 8.30766238629

Median: ma = 15.56443824163
Median: mb = 15.56443824163
Median: mc = 8.30766238629

Inradius: r = 3.61215755926
Circumradius: R = 10.17326045857

Vertex coordinates: A[20; 0] B[0; 0] C[10; 8.30766238629]
Centroid: CG[10; 2.7698874621]
Coordinates of the circumscribed circle: U[10; -1.86659807228]
Coordinates of the inscribed circle: I[10; 3.61215755926]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.2854862768° = 140°17'5″ = 0.69331599076 rad
∠ B' = β' = 140.2854862768° = 140°17'5″ = 0.69331599076 rad
∠ C' = γ' = 79.43302744637° = 79°25'49″ = 1.75552728384 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 = 13 ; ; b = 13 ; ; c = 20 ; ;

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

p = a+b+c = 13+13+20 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-13)(23-13)(23-20) } ; ; T = sqrt{ 6900 } = 83.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.07 }{ 13 } = 12.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.07 }{ 13 } = 12.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.07 }{ 20 } = 8.31 ; ;

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{ 13**2-13**2-20**2 }{ 2 * 13 * 20 } ) = 39° 42'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-13**2-20**2 }{ 2 * 13 * 20 } ) = 39° 42'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-13**2-13**2 }{ 2 * 13 * 13 } ) = 100° 34'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.07 }{ 23 } = 3.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 39° 42'55" } = 10.17 ; ;




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