16 24 26 triangle

Acute scalene triangle.

Sides: a = 16   b = 24   c = 26

Area: T = 187.9977340407
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 37.05331475504° = 37°3'11″ = 0.6476699423 rad
Angle ∠ B = β = 64.66766127554° = 64°40' = 1.12986453087 rad
Angle ∠ C = γ = 78.28802396942° = 78°16'49″ = 1.36662479219 rad

Height: ha = 23.54996675508
Height: hb = 15.66664450339
Height: hc = 14.46113338774

Median: ma = 23.70765391823
Median: mb = 17.94443584449
Median: mc = 15.71662336455

Inradius: r = 5.69768891032
Circumradius: R = 13.27767835683

Vertex coordinates: A[26; 0] B[0; 0] C[6.84661538462; 14.46113338774]
Centroid: CG[10.94987179487; 4.82204446258]
Coordinates of the circumscribed circle: U[13; 2.69768466623]
Coordinates of the inscribed circle: I[9; 5.69768891032]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.947685245° = 142°56'49″ = 0.6476699423 rad
∠ B' = β' = 115.3333387245° = 115°20' = 1.12986453087 rad
∠ C' = γ' = 101.7219760306° = 101°43'11″ = 1.36662479219 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 = 24 ; ; c = 26 ; ;

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

p = a+b+c = 16+24+26 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-16)(33-24)(33-26) } ; ; T = sqrt{ 35343 } = 188 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 188 }{ 16 } = 23.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 188 }{ 24 } = 15.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 188 }{ 26 } = 14.46 ; ;

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**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 37° 3'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 64° 40' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-24**2 }{ 2 * 24 * 16 } ) = 78° 16'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 188 }{ 33 } = 5.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 37° 3'11" } = 13.28 ; ;




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