16 17 19 triangle

Acute scalene triangle.

Sides: a = 16   b = 17   c = 19

Area: T = 127.9844374046
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 52.4177212507° = 52°25'2″ = 0.9154852943 rad
Angle ∠ B = β = 57.35221825649° = 57°21'8″ = 1.0010984419 rad
Angle ∠ C = γ = 70.23106049282° = 70°13'50″ = 1.22657552917 rad

Height: ha = 15.99880467558
Height: hb = 15.05769851819
Height: hc = 13.47220393733

Median: ma = 16.15554944214
Median: mb = 15.37704261489
Median: mc = 13.5

Inradius: r = 4.92224759249
Circumradius: R = 10.09549823729

Vertex coordinates: A[19; 0] B[0; 0] C[8.63215789474; 13.47220393733]
Centroid: CG[9.21105263158; 4.49106797911]
Coordinates of the circumscribed circle: U[9.5; 3.4144479332]
Coordinates of the inscribed circle: I[9; 4.92224759249]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.5832787493° = 127°34'58″ = 0.9154852943 rad
∠ B' = β' = 122.6487817435° = 122°38'52″ = 1.0010984419 rad
∠ C' = γ' = 109.7699395072° = 109°46'10″ = 1.22657552917 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 = 17 ; ; c = 19 ; ;

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

p = a+b+c = 16+17+19 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-16)(26-17)(26-19) } ; ; T = sqrt{ 16380 } = 127.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 127.98 }{ 16 } = 16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 127.98 }{ 17 } = 15.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 127.98 }{ 19 } = 13.47 ; ;

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{ 16**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 52° 25'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 57° 21'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 70° 13'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 127.98 }{ 26 } = 4.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 52° 25'2" } = 10.09 ; ;




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