22 25 27 triangle

Acute scalene triangle.

Sides: a = 22   b = 25   c = 27

Area: T = 258.0769758011
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 49.87659654065° = 49°52'33″ = 0.8770499814 rad
Angle ∠ B = β = 60.33435799673° = 60°20'1″ = 1.05330196199 rad
Angle ∠ C = γ = 69.79904546262° = 69°47'26″ = 1.21880732197 rad

Height: ha = 23.46108870919
Height: hb = 20.64655806409
Height: hc = 19.11662783712

Median: ma = 23.58796522451
Median: mb = 21.21990951739
Median: mc = 19.29437813816

Inradius: r = 6.97548583246
Circumradius: R = 14.38656452945

Vertex coordinates: A[27; 0] B[0; 0] C[10.88988888889; 19.11662783712]
Centroid: CG[12.63296296296; 6.37220927904]
Coordinates of the circumscribed circle: U[13.5; 4.97695865563]
Coordinates of the inscribed circle: I[12; 6.97548583246]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.1244034594° = 130°7'27″ = 0.8770499814 rad
∠ B' = β' = 119.6666420033° = 119°39'59″ = 1.05330196199 rad
∠ C' = γ' = 110.2109545374° = 110°12'34″ = 1.21880732197 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 = 22 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 22+25+27 = 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 * (37-22)(37-25)(37-27) } ; ; T = sqrt{ 66600 } = 258.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 258.07 }{ 22 } = 23.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 258.07 }{ 25 } = 20.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 258.07 }{ 27 } = 19.12 ; ;

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{ 22**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 49° 52'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 60° 20'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-22**2-25**2 }{ 2 * 25 * 22 } ) = 69° 47'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 258.07 }{ 37 } = 6.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 49° 52'33" } = 14.39 ; ;




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