8 18 18 triangle

Acute isosceles triangle.

Sides: a = 8   b = 18   c = 18

Area: T = 70.21997150991
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 25.67991768138° = 25°40'45″ = 0.44881861846 rad
Angle ∠ B = β = 77.16604115931° = 77°9'37″ = 1.34767032345 rad
Angle ∠ C = γ = 77.16604115931° = 77°9'37″ = 1.34767032345 rad

Height: ha = 17.55499287748
Height: hb = 7.87999683443
Height: hc = 7.87999683443

Median: ma = 17.55499287748
Median: mb = 10.63301458127
Median: mc = 10.63301458127

Inradius: r = 3.19108961409
Circumradius: R = 9.23108066932

Vertex coordinates: A[18; 0] B[0; 0] C[1.77877777778; 7.87999683443]
Centroid: CG[6.59325925926; 2.65999894481]
Coordinates of the circumscribed circle: U[9; 2.05112903763]
Coordinates of the inscribed circle: I[4; 3.19108961409]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.3210823186° = 154°19'15″ = 0.44881861846 rad
∠ B' = β' = 102.8439588407° = 102°50'23″ = 1.34767032345 rad
∠ C' = γ' = 102.8439588407° = 102°50'23″ = 1.34767032345 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 = 18 ; ; c = 18 ; ;

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

p = a+b+c = 8+18+18 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-8)(22-18)(22-18) } ; ; T = sqrt{ 4928 } = 70.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.2 }{ 8 } = 17.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.2 }{ 18 } = 7.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.2 }{ 18 } = 7.8 ; ;

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**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 25° 40'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-8**2-18**2 }{ 2 * 8 * 18 } ) = 77° 9'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-8**2-18**2 }{ 2 * 18 * 8 } ) = 77° 9'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.2 }{ 22 } = 3.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 25° 40'45" } = 9.23 ; ;




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