18 30 30 triangle

Acute isosceles triangle.

Sides: a = 18   b = 30   c = 30

Area: T = 257.5643584383
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 34.91552062474° = 34°54'55″ = 0.6099385308 rad
Angle ∠ B = β = 72.54223968763° = 72°32'33″ = 1.26661036728 rad
Angle ∠ C = γ = 72.54223968763° = 72°32'33″ = 1.26661036728 rad

Height: ha = 28.61881760425
Height: hb = 17.17109056255
Height: hc = 17.17109056255

Median: ma = 28.61881760425
Median: mb = 19.67223155729
Median: mc = 19.67223155729

Inradius: r = 6.60441944713
Circumradius: R = 15.72442725508

Vertex coordinates: A[30; 0] B[0; 0] C[5.4; 17.17109056255]
Centroid: CG[11.8; 5.72436352085]
Coordinates of the circumscribed circle: U[15; 4.71772817652]
Coordinates of the inscribed circle: I[9; 6.60441944713]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.0854793753° = 145°5'5″ = 0.6099385308 rad
∠ B' = β' = 107.4587603124° = 107°27'27″ = 1.26661036728 rad
∠ C' = γ' = 107.4587603124° = 107°27'27″ = 1.26661036728 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 = 30 ; ; c = 30 ; ;

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

p = a+b+c = 18+30+30 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-18)(39-30)(39-30) } ; ; T = sqrt{ 66339 } = 257.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 257.56 }{ 18 } = 28.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 257.56 }{ 30 } = 17.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 257.56 }{ 30 } = 17.17 ; ;

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**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 34° 54'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 72° 32'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-30**2 }{ 2 * 30 * 18 } ) = 72° 32'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 257.56 }{ 39 } = 6.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 34° 54'55" } = 15.72 ; ;




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