9 9 13 triangle

Obtuse isosceles triangle.

Sides: a = 9   b = 9   c = 13

Area: T = 40.46221736935
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 43.76217426927° = 43°45'42″ = 0.76437864964 rad
Angle ∠ B = β = 43.76217426927° = 43°45'42″ = 0.76437864964 rad
Angle ∠ C = γ = 92.47765146146° = 92°28'35″ = 1.61440196608 rad

Height: ha = 8.99215941541
Height: hb = 8.99215941541
Height: hc = 6.2254949799

Median: ma = 10.23547447452
Median: mb = 10.23547447452
Median: mc = 6.2254949799

Inradius: r = 2.61104628189
Circumradius: R = 6.50660765641

Vertex coordinates: A[13; 0] B[0; 0] C[6.5; 6.2254949799]
Centroid: CG[6.5; 2.07549832663]
Coordinates of the circumscribed circle: U[6.5; -0.28111267651]
Coordinates of the inscribed circle: I[6.5; 2.61104628189]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.2388257307° = 136°14'18″ = 0.76437864964 rad
∠ B' = β' = 136.2388257307° = 136°14'18″ = 0.76437864964 rad
∠ C' = γ' = 87.52334853854° = 87°31'25″ = 1.61440196608 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 = 9 ; ; b = 9 ; ; c = 13 ; ;

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

p = a+b+c = 9+9+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 * (15.5-9)(15.5-9)(15.5-13) } ; ; T = sqrt{ 1637.19 } = 40.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.46 }{ 9 } = 8.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.46 }{ 9 } = 8.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.46 }{ 13 } = 6.22 ; ;

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{ 9**2-9**2-13**2 }{ 2 * 9 * 13 } ) = 43° 45'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-9**2-13**2 }{ 2 * 9 * 13 } ) = 43° 45'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-9**2-9**2 }{ 2 * 9 * 9 } ) = 92° 28'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.46 }{ 15.5 } = 2.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 43° 45'42" } = 6.51 ; ;




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