18 23 28 triangle

Acute scalene triangle.

Sides: a = 18   b = 23   c = 28

Area: T = 206.2879997818
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 39.83881498056° = 39°50'17″ = 0.6955306882 rad
Angle ∠ B = β = 54.94220420416° = 54°56'31″ = 0.95989195314 rad
Angle ∠ C = γ = 85.22198081528° = 85°13'11″ = 1.48773662402 rad

Height: ha = 22.92199997576
Height: hb = 17.93773911147
Height: hc = 14.73442855585

Median: ma = 23.99895810718
Median: mb = 20.53765527779
Median: mc = 15.18222264507

Inradius: r = 5.97991303716
Circumradius: R = 14.04988657681

Vertex coordinates: A[28; 0] B[0; 0] C[10.33992857143; 14.73442855585]
Centroid: CG[12.78797619048; 4.91114285195]
Coordinates of the circumscribed circle: U[14; 1.1710738814]
Coordinates of the inscribed circle: I[11.5; 5.97991303716]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.1621850194° = 140°9'43″ = 0.6955306882 rad
∠ B' = β' = 125.0587957958° = 125°3'29″ = 0.95989195314 rad
∠ C' = γ' = 94.78801918472° = 94°46'49″ = 1.48773662402 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 = 23 ; ; c = 28 ; ;

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

p = a+b+c = 18+23+28 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-18)(34.5-23)(34.5-28) } ; ; T = sqrt{ 42551.44 } = 206.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 206.28 }{ 18 } = 22.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 206.28 }{ 23 } = 17.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 206.28 }{ 28 } = 14.73 ; ;

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**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 39° 50'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 54° 56'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-23**2 }{ 2 * 23 * 18 } ) = 85° 13'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 206.28 }{ 34.5 } = 5.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 39° 50'17" } = 14.05 ; ;




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