18 27 28 triangle

Acute scalene triangle.

Sides: a = 18   b = 27   c = 28

Area: T = 233.5098966637
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 38.15219102718° = 38°9'7″ = 0.66658764502 rad
Angle ∠ B = β = 67.91443583076° = 67°54'52″ = 1.18553291618 rad
Angle ∠ C = γ = 73.93437314206° = 73°56'1″ = 1.29903870416 rad

Height: ha = 25.94554407375
Height: hb = 17.29769604916
Height: hc = 16.67992119027

Median: ma = 25.99903828367
Median: mb = 19.28108194847
Median: mc = 18.18796589627

Inradius: r = 6.39875059353
Circumradius: R = 14.56990336821

Vertex coordinates: A[28; 0] B[0; 0] C[6.76878571429; 16.67992119027]
Centroid: CG[11.58992857143; 5.56597373009]
Coordinates of the circumscribed circle: U[14; 4.03219650828]
Coordinates of the inscribed circle: I[9.5; 6.39875059353]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.8488089728° = 141°50'53″ = 0.66658764502 rad
∠ B' = β' = 112.0865641692° = 112°5'8″ = 1.18553291618 rad
∠ C' = γ' = 106.0666268579° = 106°3'59″ = 1.29903870416 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 = 27 ; ; c = 28 ; ;

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

p = a+b+c = 18+27+28 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-18)(36.5-27)(36.5-28) } ; ; T = sqrt{ 54526.44 } = 233.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 233.51 }{ 18 } = 25.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 233.51 }{ 27 } = 17.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 233.51 }{ 28 } = 16.68 ; ;

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**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 38° 9'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 67° 54'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-27**2 }{ 2 * 27 * 18 } ) = 73° 56'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 233.51 }{ 36.5 } = 6.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 38° 9'7" } = 14.57 ; ;




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