16 20 25 triangle

Acute scalene triangle.

Sides: a = 16   b = 20   c = 25

Area: T = 159.8122194466
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 39.73658255397° = 39°44'9″ = 0.69435209867 rad
Angle ∠ B = β = 53.04105251447° = 53°2'26″ = 0.92657318008 rad
Angle ∠ C = γ = 87.22436493156° = 87°13'25″ = 1.52223398662 rad

Height: ha = 19.97765243082
Height: hb = 15.98112194466
Height: hc = 12.78549755573

Median: ma = 21.17878185845
Median: mb = 18.45326420872
Median: mc = 13.10553424221

Inradius: r = 5.24397440808
Circumradius: R = 12.51546895497

Vertex coordinates: A[25; 0] B[0; 0] C[9.62; 12.78549755573]
Centroid: CG[11.54; 4.26216585191]
Coordinates of the circumscribed circle: U[12.5; 0.60661802751]
Coordinates of the inscribed circle: I[10.5; 5.24397440808]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.264417446° = 140°15'51″ = 0.69435209867 rad
∠ B' = β' = 126.9599474855° = 126°57'34″ = 0.92657318008 rad
∠ C' = γ' = 92.77663506844° = 92°46'35″ = 1.52223398662 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 = 20 ; ; c = 25 ; ;

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

p = a+b+c = 16+20+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 * (30.5-16)(30.5-20)(30.5-25) } ; ; T = sqrt{ 25539.94 } = 159.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 159.81 }{ 16 } = 19.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 159.81 }{ 20 } = 15.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 159.81 }{ 25 } = 12.78 ; ;

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**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 39° 44'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 53° 2'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-16**2-20**2 }{ 2 * 20 * 16 } ) = 87° 13'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 159.81 }{ 30.5 } = 5.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 39° 44'9" } = 12.51 ; ;




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