10 16 25 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 16   c = 25

Area: T = 43.32994068734
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 12.51221731473° = 12°30'44″ = 0.2188378618 rad
Angle ∠ B = β = 20.2821649813° = 20°16'54″ = 0.3543981567 rad
Angle ∠ C = γ = 147.206617704° = 147°12'22″ = 2.56992324686 rad

Height: ha = 8.66658813747
Height: hb = 5.41661758592
Height: hc = 3.46663525499

Median: ma = 20.38438171106
Median: mb = 17.27771525432
Median: mc = 4.66436895265

Inradius: r = 1.69991924264
Circumradius: R = 23.07990142806

Vertex coordinates: A[25; 0] B[0; 0] C[9.38; 3.46663525499]
Centroid: CG[11.46; 1.155545085]
Coordinates of the circumscribed circle: U[12.5; -19.40107963796]
Coordinates of the inscribed circle: I[9.5; 1.69991924264]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.4887826853° = 167°29'16″ = 0.2188378618 rad
∠ B' = β' = 159.7188350187° = 159°43'6″ = 0.3543981567 rad
∠ C' = γ' = 32.79438229603° = 32°47'38″ = 2.56992324686 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 = 10 ; ; b = 16 ; ; c = 25 ; ;

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

p = a+b+c = 10+16+25 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-10)(25.5-16)(25.5-25) } ; ; T = sqrt{ 1877.44 } = 43.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.33 }{ 10 } = 8.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.33 }{ 16 } = 5.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.33 }{ 25 } = 3.47 ; ;

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{ 10**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 12° 30'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-10**2-25**2 }{ 2 * 10 * 25 } ) = 20° 16'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-10**2-16**2 }{ 2 * 16 * 10 } ) = 147° 12'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.33 }{ 25.5 } = 1.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 12° 30'44" } = 23.08 ; ;




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