38 45.5 55 triangle

Acute scalene triangle.

Sides: a = 38   b = 45.5   c = 55

Area: T = 855.8043658758
Perimeter: p = 138.5
Semiperimeter: s = 69.25

Angle ∠ A = α = 43.15437907868° = 43°9'14″ = 0.75331757339 rad
Angle ∠ B = β = 54.98799092618° = 54°58'48″ = 0.96595804391 rad
Angle ∠ C = γ = 81.86662999515° = 81°51'59″ = 1.42988364806 rad

Height: ha = 45.04222978294
Height: hb = 37.61877432421
Height: hc = 31.12201330457

Median: ma = 46.76113622556
Median: mb = 41.43659445409
Median: mc = 31.63766085414

Inradius: r = 12.35881755777
Circumradius: R = 27.7799444218

Vertex coordinates: A[55; 0] B[0; 0] C[21.80768181818; 31.12201330457]
Centroid: CG[25.60222727273; 10.37333776819]
Coordinates of the circumscribed circle: U[27.5; 3.93303334539]
Coordinates of the inscribed circle: I[23.75; 12.35881755777]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.8466209213° = 136°50'46″ = 0.75331757339 rad
∠ B' = β' = 125.0220090738° = 125°1'12″ = 0.96595804391 rad
∠ C' = γ' = 98.13437000485° = 98°8'1″ = 1.42988364806 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 = 38 ; ; b = 45.5 ; ; c = 55 ; ;

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

p = a+b+c = 38+45.5+55 = 138.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 138.5 }{ 2 } = 69.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 69.25 * (69.25-38)(69.25-45.5)(69.25-55) } ; ; T = sqrt{ 732399.9 } = 855.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 855.8 }{ 38 } = 45.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 855.8 }{ 45.5 } = 37.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 855.8 }{ 55 } = 31.12 ; ;

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{ 38**2-45.5**2-55**2 }{ 2 * 45.5 * 55 } ) = 43° 9'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 45.5**2-38**2-55**2 }{ 2 * 38 * 55 } ) = 54° 58'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 55**2-38**2-45.5**2 }{ 2 * 45.5 * 38 } ) = 81° 51'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 855.8 }{ 69.25 } = 12.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38 }{ 2 * sin 43° 9'14" } = 27.78 ; ;




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