9 19 24 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 19   c = 24

Area: T = 78.66438417572
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 20.18328243451° = 20°10'58″ = 0.35222567372 rad
Angle ∠ B = β = 46.75498273458° = 46°44'59″ = 0.81659384119 rad
Angle ∠ C = γ = 113.0677348309° = 113°4'2″ = 1.97333975045 rad

Height: ha = 17.48108537238
Height: hb = 8.28804043955
Height: hc = 6.55553201464

Median: ma = 21.17219153597
Median: mb = 15.43553490404
Median: mc = 8.77549643874

Inradius: r = 3.02655323753
Circumradius: R = 13.0432841248

Vertex coordinates: A[24; 0] B[0; 0] C[6.16766666667; 6.55553201464]
Centroid: CG[10.05655555556; 2.18551067155]
Coordinates of the circumscribed circle: U[12; -5.11103530036]
Coordinates of the inscribed circle: I[7; 3.02655323753]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.8177175655° = 159°49'2″ = 0.35222567372 rad
∠ B' = β' = 133.2550172654° = 133°15'1″ = 0.81659384119 rad
∠ C' = γ' = 66.93326516909° = 66°55'58″ = 1.97333975045 rad

Calculate another triangle




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 = 19 ; ; c = 24 ; ;

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

p = a+b+c = 9+19+24 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-9)(26-19)(26-24) } ; ; T = sqrt{ 6188 } = 78.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.66 }{ 9 } = 17.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.66 }{ 19 } = 8.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.66 }{ 24 } = 6.56 ; ;

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**2-19**2-24**2 }{ 2 * 19 * 24 } ) = 20° 10'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-9**2-24**2 }{ 2 * 9 * 24 } ) = 46° 44'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-9**2-19**2 }{ 2 * 19 * 9 } ) = 113° 4'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.66 }{ 26 } = 3.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 20° 10'58" } = 13.04 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.