18 27 29 triangle

Acute scalene triangle.

Sides: a = 18   b = 27   c = 29

Area: T = 237.1549741724
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 37.28325762069° = 37°16'57″ = 0.65107037084 rad
Angle ∠ B = β = 65.31552958388° = 65°18'55″ = 1.14399669643 rad
Angle ∠ C = γ = 77.40221279543° = 77°24'8″ = 1.35109219809 rad

Height: ha = 26.35499713027
Height: hb = 17.56766475351
Height: hc = 16.35551546017

Median: ma = 26.53329983228
Median: mb = 20.00662490237
Median: mc = 17.78334192438

Inradius: r = 6.4099452479
Circumradius: R = 14.85877011907

Vertex coordinates: A[29; 0] B[0; 0] C[7.51772413793; 16.35551546017]
Centroid: CG[12.17224137931; 5.45217182006]
Coordinates of the circumscribed circle: U[14.5; 3.24105685725]
Coordinates of the inscribed circle: I[10; 6.4099452479]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.7177423793° = 142°43'3″ = 0.65107037084 rad
∠ B' = β' = 114.6854704161° = 114°41'5″ = 1.14399669643 rad
∠ C' = γ' = 102.5987872046° = 102°35'52″ = 1.35109219809 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 = 29 ; ;

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

p = a+b+c = 18+27+29 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-18)(37-27)(37-29) } ; ; T = sqrt{ 56240 } = 237.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 237.15 }{ 18 } = 26.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 237.15 }{ 27 } = 17.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 237.15 }{ 29 } = 16.36 ; ;

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**2-29**2 }{ 2 * 27 * 29 } ) = 37° 16'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-18**2-29**2 }{ 2 * 18 * 29 } ) = 65° 18'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-18**2-27**2 }{ 2 * 27 * 18 } ) = 77° 24'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 237.15 }{ 37 } = 6.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 37° 16'57" } = 14.86 ; ;




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