1 18 18 triangle

Acute isosceles triangle.

Sides: a = 1   b = 18   c = 18

Area: T = 8.99765271077
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 3.18435083532° = 3°11'1″ = 0.05655627025 rad
Angle ∠ B = β = 88.40882458234° = 88°24'30″ = 1.54330149755 rad
Angle ∠ C = γ = 88.40882458234° = 88°24'30″ = 1.54330149755 rad

Height: ha = 17.99330542154
Height: hb = 10.9996141231
Height: hc = 10.9996141231

Median: ma = 17.99330542154
Median: mb = 9.02877350426
Median: mc = 9.02877350426

Inradius: r = 0.48662987626
Circumradius: R = 9.00334742329

Vertex coordinates: A[18; 0] B[0; 0] C[0.02877777778; 10.9996141231]
Centroid: CG[6.00992592593; 0.33332047077]
Coordinates of the circumscribed circle: U[9; 0.25500965065]
Coordinates of the inscribed circle: I[0.5; 0.48662987626]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.8166491647° = 176°48'59″ = 0.05655627025 rad
∠ B' = β' = 91.59217541766° = 91°35'30″ = 1.54330149755 rad
∠ C' = γ' = 91.59217541766° = 91°35'30″ = 1.54330149755 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 = 1 ; ; b = 18 ; ; c = 18 ; ;

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

p = a+b+c = 1+18+18 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-1)(18.5-18)(18.5-18) } ; ; T = sqrt{ 80.94 } = 9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9 }{ 1 } = 17.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9 }{ 18 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9 }{ 18 } = 1 ; ;

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{ 1**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 3° 11'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-1**2-18**2 }{ 2 * 1 * 18 } ) = 88° 24'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-1**2-18**2 }{ 2 * 18 * 1 } ) = 88° 24'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9 }{ 18.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 3° 11'1" } = 9 ; ;




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