3 18 19 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 18   c = 19

Area: T = 26.07768096208
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 8.77215990616° = 8°46'18″ = 0.15330932843 rad
Angle ∠ B = β = 66.20222871793° = 66°12'8″ = 1.15554478836 rad
Angle ∠ C = γ = 105.0266113759° = 105°1'34″ = 1.83330514857 rad

Height: ha = 17.38545397472
Height: hb = 2.89774232912
Height: hc = 2.74549273285

Median: ma = 18.44658667457
Median: mb = 10.19880390272
Median: mc = 8.73221245983

Inradius: r = 1.3043840481
Circumradius: R = 9.8366325982

Vertex coordinates: A[19; 0] B[0; 0] C[1.21105263158; 2.74549273285]
Centroid: CG[6.73768421053; 0.91549757762]
Coordinates of the circumscribed circle: U[9.5; -2.55501585879]
Coordinates of the inscribed circle: I[2; 1.3043840481]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.2288400938° = 171°13'42″ = 0.15330932843 rad
∠ B' = β' = 113.7987712821° = 113°47'52″ = 1.15554478836 rad
∠ C' = γ' = 74.97438862409° = 74°58'26″ = 1.83330514857 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 = 3 ; ; b = 18 ; ; c = 19 ; ;

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

p = a+b+c = 3+18+19 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-3)(20-18)(20-19) } ; ; T = sqrt{ 680 } = 26.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.08 }{ 3 } = 17.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.08 }{ 18 } = 2.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.08 }{ 19 } = 2.74 ; ;

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{ 3**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 8° 46'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-3**2-19**2 }{ 2 * 3 * 19 } ) = 66° 12'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-3**2-18**2 }{ 2 * 18 * 3 } ) = 105° 1'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.08 }{ 20 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 8° 46'18" } = 9.84 ; ;




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