16 21 25 triangle

Acute scalene triangle.

Sides: a = 16   b = 21   c = 25

Area: T = 167.0332930885
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 39.51876527972° = 39°31'4″ = 0.6989713154 rad
Angle ∠ B = β = 56.63329870308° = 56°37'59″ = 0.98884320889 rad
Angle ∠ C = γ = 83.84993601721° = 83°50'58″ = 1.46334474107 rad

Height: ha = 20.87991163606
Height: hb = 15.90878981795
Height: hc = 13.36326344708

Median: ma = 21.65664078277
Median: mb = 18.17327818454
Median: mc = 13.86554246239

Inradius: r = 5.38881590608
Circumradius: R = 12.57223711419

Vertex coordinates: A[25; 0] B[0; 0] C[8.8; 13.36326344708]
Centroid: CG[11.26766666667; 4.45442114903]
Coordinates of the circumscribed circle: U[12.5; 1.34770397652]
Coordinates of the inscribed circle: I[10; 5.38881590608]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.4822347203° = 140°28'56″ = 0.6989713154 rad
∠ B' = β' = 123.3677012969° = 123°22'1″ = 0.98884320889 rad
∠ C' = γ' = 96.15106398279° = 96°9'2″ = 1.46334474107 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 = 21 ; ; c = 25 ; ;

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

p = a+b+c = 16+21+25 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-16)(31-21)(31-25) } ; ; T = sqrt{ 27900 } = 167.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 167.03 }{ 16 } = 20.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 167.03 }{ 21 } = 15.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 167.03 }{ 25 } = 13.36 ; ;

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**2-21**2-25**2 }{ 2 * 21 * 25 } ) = 39° 31'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 56° 37'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-16**2-21**2 }{ 2 * 21 * 16 } ) = 83° 50'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 167.03 }{ 31 } = 5.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 39° 31'4" } = 12.57 ; ;




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