10 18 19 triangle

Acute scalene triangle.

Sides: a = 10   b = 18   c = 19

Area: T = 88.61111590038
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 31.21111804983° = 31°12'40″ = 0.54547378631 rad
Angle ∠ B = β = 68.86774776095° = 68°52'3″ = 1.20219642318 rad
Angle ∠ C = γ = 79.92113418922° = 79°55'17″ = 1.39548905586 rad

Height: ha = 17.72222318008
Height: hb = 9.84656843338
Height: hc = 9.32774904215

Median: ma = 17.81985296812
Median: mb = 12.22770192606
Median: mc = 11.03440382454

Inradius: r = 3.77106876172
Circumradius: R = 9.64988976063

Vertex coordinates: A[19; 0] B[0; 0] C[3.60552631579; 9.32774904215]
Centroid: CG[7.53550877193; 3.10991634738]
Coordinates of the circumscribed circle: U[9.5; 1.68985570811]
Coordinates of the inscribed circle: I[5.5; 3.77106876172]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.7898819502° = 148°47'20″ = 0.54547378631 rad
∠ B' = β' = 111.133252239° = 111°7'57″ = 1.20219642318 rad
∠ C' = γ' = 100.0798658108° = 100°4'43″ = 1.39548905586 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 = 18 ; ; c = 19 ; ;

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

p = a+b+c = 10+18+19 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-10)(23.5-18)(23.5-19) } ; ; T = sqrt{ 7851.94 } = 88.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.61 }{ 10 } = 17.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.61 }{ 18 } = 9.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.61 }{ 19 } = 9.33 ; ;

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**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 31° 12'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 68° 52'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-10**2-18**2 }{ 2 * 18 * 10 } ) = 79° 55'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.61 }{ 23.5 } = 3.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 31° 12'40" } = 9.65 ; ;




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