14 22 25 triangle

Acute scalene triangle.

Sides: a = 14   b = 22   c = 25

Area: T = 153.3854932441
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 33.90112619969° = 33°54'5″ = 0.59216886424 rad
Angle ∠ B = β = 61.22112541029° = 61°13'16″ = 1.06985124563 rad
Angle ∠ C = γ = 84.87774839002° = 84°52'39″ = 1.48113915549 rad

Height: ha = 21.91221332059
Height: hb = 13.94440847674
Height: hc = 12.27107945953

Median: ma = 22.48333271559
Median: mb = 17.01546995272
Median: mc = 13.55554417117

Inradius: r = 5.02990141784
Circumradius: R = 12.55501245094

Vertex coordinates: A[25; 0] B[0; 0] C[6.74; 12.27107945953]
Centroid: CG[10.58; 4.09902648651]
Coordinates of the circumscribed circle: U[12.5; 1.12105468312]
Coordinates of the inscribed circle: I[8.5; 5.02990141784]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.0998738003° = 146°5'55″ = 0.59216886424 rad
∠ B' = β' = 118.7798745897° = 118°46'43″ = 1.06985124563 rad
∠ C' = γ' = 95.12325160998° = 95°7'21″ = 1.48113915549 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 = 14 ; ; b = 22 ; ; c = 25 ; ;

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

p = a+b+c = 14+22+25 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-14)(30.5-22)(30.5-25) } ; ; T = sqrt{ 23526.94 } = 153.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 153.38 }{ 14 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 153.38 }{ 22 } = 13.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 153.38 }{ 25 } = 12.27 ; ;

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{ 14**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 33° 54'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 61° 13'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-22**2 }{ 2 * 22 * 14 } ) = 84° 52'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 153.38 }{ 30.5 } = 5.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 33° 54'5" } = 12.55 ; ;




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