18 18 30 triangle

Obtuse isosceles triangle.

Sides: a = 18   b = 18   c = 30

Area: T = 149.2488115566
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 112.8855380476° = 112°53'7″ = 1.97702215667 rad

Height: ha = 16.58331239518
Height: hb = 16.58331239518
Height: hc = 9.95498743711

Median: ma = 23.04334372436
Median: mb = 23.04334372436
Median: mc = 9.95498743711

Inradius: r = 4.52326701687
Circumradius: R = 16.28216126072

Vertex coordinates: A[30; 0] B[0; 0] C[15; 9.95498743711]
Centroid: CG[15; 3.31766247904]
Coordinates of the circumscribed circle: U[15; -6.33217382361]
Coordinates of the inscribed circle: I[15; 4.52326701687]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 67.11546195238° = 67°6'53″ = 1.97702215667 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 = 30 ; ;

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

p = a+b+c = 18+18+30 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-18)(33-18)(33-30) } ; ; T = sqrt{ 22275 } = 149.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 149.25 }{ 18 } = 16.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 149.25 }{ 18 } = 16.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 149.25 }{ 30 } = 9.95 ; ;

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**2-30**2 }{ 2 * 18 * 30 } ) = 33° 33'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 33° 33'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 112° 53'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 149.25 }{ 33 } = 4.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 33° 33'26" } = 16.28 ; ;




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