16 22 25 triangle

Acute scalene triangle.

Sides: a = 16   b = 22   c = 25

Area: T = 173.6365933781
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 39.15437385766° = 39°9'13″ = 0.68333616526 rad
Angle ∠ B = β = 60.24877894243° = 60°14'52″ = 1.05215222925 rad
Angle ∠ C = γ = 80.59884719991° = 80°35'54″ = 1.40767087085 rad

Height: ha = 21.70444917226
Height: hb = 15.78550848892
Height: hc = 13.89108747025

Median: ma = 22.14772345904
Median: mb = 17.87545629317
Median: mc = 14.62201915172

Inradius: r = 5.51222518661
Circumradius: R = 12.67701884345

Vertex coordinates: A[25; 0] B[0; 0] C[7.94; 13.89108747025]
Centroid: CG[10.98; 4.63302915675]
Coordinates of the circumscribed circle: U[12.5; 2.07697040767]
Coordinates of the inscribed circle: I[9.5; 5.51222518661]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.8466261423° = 140°50'47″ = 0.68333616526 rad
∠ B' = β' = 119.7522210576° = 119°45'8″ = 1.05215222925 rad
∠ C' = γ' = 99.40215280009° = 99°24'6″ = 1.40767087085 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 = 16 ; ; b = 22 ; ; c = 25 ; ;

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

p = a+b+c = 16+22+25 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-16)(31.5-22)(31.5-25) } ; ; T = sqrt{ 30149.44 } = 173.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 173.64 }{ 16 } = 21.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 173.64 }{ 22 } = 15.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 173.64 }{ 25 } = 13.89 ; ;

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{ 16**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 39° 9'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 60° 14'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-16**2-22**2 }{ 2 * 22 * 16 } ) = 80° 35'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 173.64 }{ 31.5 } = 5.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 39° 9'13" } = 12.67 ; ;




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