18 18 26 triangle

Obtuse isosceles triangle.

Sides: a = 18   b = 18   c = 26

Area: T = 161.8498694774
Perimeter: p = 62
Semiperimeter: s = 31

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 = 17.98331883082
Height: hb = 17.98331883082
Height: hc = 12.4549899598

Median: ma = 20.46994894905
Median: mb = 20.46994894905
Median: mc = 12.4549899598

Inradius: r = 5.22109256379
Circumradius: R = 13.01221531282

Vertex coordinates: A[26; 0] B[0; 0] C[13; 12.4549899598]
Centroid: CG[13; 4.15499665327]
Coordinates of the circumscribed circle: U[13; -0.56222535302]
Coordinates of the inscribed circle: I[13; 5.22109256379]

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 = 18 ; ; b = 18 ; ; c = 26 ; ;

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

p = a+b+c = 18+18+26 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-18)(31-18)(31-26) } ; ; T = sqrt{ 26195 } = 161.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161.85 }{ 18 } = 17.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161.85 }{ 18 } = 17.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161.85 }{ 26 } = 12.45 ; ;

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{ 18**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 43° 45'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 43° 45'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 92° 28'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161.85 }{ 31 } = 5.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 43° 45'42" } = 13.01 ; ;




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