8 19 24 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 19   c = 24

Area: T = 65.96216365776
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 16.81663773207° = 16°48'59″ = 0.29435011525 rad
Angle ∠ B = β = 43.40110149198° = 43°24'4″ = 0.75774906091 rad
Angle ∠ C = γ = 119.7832607759° = 119°46'57″ = 2.0910600892 rad

Height: ha = 16.49904091444
Height: hb = 6.94333301661
Height: hc = 5.49768030481

Median: ma = 21.27220473862
Median: mb = 15.15875063912
Median: mc = 8.27664726786

Inradius: r = 2.58767308462
Circumradius: R = 13.82662185009

Vertex coordinates: A[24; 0] B[0; 0] C[5.81325; 5.49768030481]
Centroid: CG[9.93875; 1.83222676827]
Coordinates of the circumscribed circle: U[12; -6.86876282685]
Coordinates of the inscribed circle: I[6.5; 2.58767308462]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.1843622679° = 163°11'1″ = 0.29435011525 rad
∠ B' = β' = 136.599898508° = 136°35'56″ = 0.75774906091 rad
∠ C' = γ' = 60.21773922406° = 60°13'3″ = 2.0910600892 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 = 8 ; ; b = 19 ; ; c = 24 ; ;

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

p = a+b+c = 8+19+24 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-8)(25.5-19)(25.5-24) } ; ; T = sqrt{ 4350.94 } = 65.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.96 }{ 8 } = 16.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.96 }{ 19 } = 6.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.96 }{ 24 } = 5.5 ; ;

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{ 8**2-19**2-24**2 }{ 2 * 19 * 24 } ) = 16° 48'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-8**2-24**2 }{ 2 * 8 * 24 } ) = 43° 24'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-8**2-19**2 }{ 2 * 19 * 8 } ) = 119° 46'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.96 }{ 25.5 } = 2.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 16° 48'59" } = 13.83 ; ;




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