10 16 19 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 16   c = 19

Area: T = 79.99902337789
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 31.75325344486° = 31°45'9″ = 0.5544186272 rad
Angle ∠ B = β = 57.35221825649° = 57°21'8″ = 1.0010984419 rad
Angle ∠ C = γ = 90.89552829866° = 90°53'43″ = 1.58664219626 rad

Height: ha = 15.99880467558
Height: hb = 9.99987792224
Height: hc = 8.42200246083

Median: ma = 16.83774582405
Median: mb = 12.90334879006
Median: mc = 9.36774969976

Inradius: r = 3.55551215013
Circumradius: R = 9.50111598804

Vertex coordinates: A[19; 0] B[0; 0] C[5.39547368421; 8.42200246083]
Centroid: CG[8.13215789474; 2.80766748694]
Coordinates of the circumscribed circle: U[9.5; -0.14884556231]
Coordinates of the inscribed circle: I[6.5; 3.55551215013]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2477465551° = 148°14'51″ = 0.5544186272 rad
∠ B' = β' = 122.6487817435° = 122°38'52″ = 1.0010984419 rad
∠ C' = γ' = 89.10547170134° = 89°6'17″ = 1.58664219626 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 = 19 ; ;

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

p = a+b+c = 10+16+19 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-10)(22.5-16)(22.5-19) } ; ; T = sqrt{ 6398.44 } = 79.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.99 }{ 10 } = 16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.99 }{ 16 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.99 }{ 19 } = 8.42 ; ;

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**2-19**2 }{ 2 * 16 * 19 } ) = 31° 45'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 57° 21'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-10**2-16**2 }{ 2 * 16 * 10 } ) = 90° 53'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.99 }{ 22.5 } = 3.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 31° 45'9" } = 9.5 ; ;




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