18 19 24 triangle

Acute scalene triangle.

Sides: a = 18   b = 19   c = 24

Area: T = 168.8154802372
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 47.76768473923° = 47°46'1″ = 0.83436887603 rad
Angle ∠ B = β = 51.40327128396° = 51°24'10″ = 0.89771465835 rad
Angle ∠ C = γ = 80.83304397681° = 80°49'50″ = 1.41107573098 rad

Height: ha = 18.75772002636
Height: hb = 17.77699791971
Height: hc = 14.06879001977

Median: ma = 19.6855019685
Median: mb = 18.96770767384
Median: mc = 14.08990028036

Inradius: r = 5.53549115532
Circumradius: R = 12.15553321816

Vertex coordinates: A[24; 0] B[0; 0] C[11.22991666667; 14.06879001977]
Centroid: CG[11.74330555556; 4.68993000659]
Coordinates of the circumscribed circle: U[12; 1.93770339295]
Coordinates of the inscribed circle: I[11.5; 5.53549115532]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.2333152608° = 132°13'59″ = 0.83436887603 rad
∠ B' = β' = 128.597728716° = 128°35'50″ = 0.89771465835 rad
∠ C' = γ' = 99.17695602319° = 99°10'10″ = 1.41107573098 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 = 18 ; ; b = 19 ; ; c = 24 ; ;

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

p = a+b+c = 18+19+24 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-18)(30.5-19)(30.5-24) } ; ; T = sqrt{ 28498.44 } = 168.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 168.81 }{ 18 } = 18.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 168.81 }{ 19 } = 17.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 168.81 }{ 24 } = 14.07 ; ;

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{ 18**2-19**2-24**2 }{ 2 * 19 * 24 } ) = 47° 46'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 51° 24'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-18**2-19**2 }{ 2 * 19 * 18 } ) = 80° 49'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 168.81 }{ 30.5 } = 5.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 47° 46'1" } = 12.16 ; ;




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