9 18 19 triangle

Acute scalene triangle.

Sides: a = 9   b = 18   c = 19

Area: T = 80.2549610591
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 27.989860602° = 27°59'19″ = 0.48884933281 rad
Angle ∠ B = β = 69.81664193194° = 69°48'59″ = 1.21985263891 rad
Angle ∠ C = γ = 82.19549746606° = 82°11'42″ = 1.43545729364 rad

Height: ha = 17.8333246798
Height: hb = 8.9176623399
Height: hc = 8.44773274306

Median: ma = 17.9511323071
Median: mb = 11.83221595662
Median: mc = 10.59548100502

Inradius: r = 3.4899113504
Circumradius: R = 9.5898831576

Vertex coordinates: A[19; 0] B[0; 0] C[3.10552631579; 8.44773274306]
Centroid: CG[7.36884210526; 2.81657758102]
Coordinates of the circumscribed circle: U[9.5; 1.30221870042]
Coordinates of the inscribed circle: I[5; 3.4899113504]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.011139398° = 152°41″ = 0.48884933281 rad
∠ B' = β' = 110.1843580681° = 110°11'1″ = 1.21985263891 rad
∠ C' = γ' = 97.80550253394° = 97°48'18″ = 1.43545729364 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 = 9 ; ; b = 18 ; ; c = 19 ; ;

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

p = a+b+c = 9+18+19 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-9)(23-18)(23-19) } ; ; T = sqrt{ 6440 } = 80.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 80.25 }{ 9 } = 17.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 80.25 }{ 18 } = 8.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 80.25 }{ 19 } = 8.45 ; ;

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{ 9**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 27° 59'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-9**2-19**2 }{ 2 * 9 * 19 } ) = 69° 48'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-9**2-18**2 }{ 2 * 18 * 9 } ) = 82° 11'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 80.25 }{ 23 } = 3.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 27° 59'19" } = 9.59 ; ;




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