Respuesta :
A typical windmill has three blades. We can envision these blades in a circle, which a circle = 360 degrees. We want to divide up the angles of the blades so they are even or makes up 360 degrees. We have three blades so we have 3 angles to divide by 360 degrees. So, 360 / 3 = 120 degrees. Now that we know the angle of the blades, we can use the Law of Cos to solve the distance between the blade tip.
Law of Cos
[tex]c^2 = a^2 + b^2 - 2(a)(b)(\cos A)[/tex]
We know
a = 20
b = 20
A = Angle = 120
We need to solve for c
[tex]c^2 = a^2 + b^2 - 2(a)(b)(\cos A)[/tex]
Take the square root of each side of the =
[tex]\sqrt{c^2} = \sqrt{a^2 + b^2 - 2(a)(b)(\cos A)}[/tex]
[tex]c = \sqrt{a^2 + b^2 - 2(a)(b)(\cos A)}[/tex]
Input the values we know into the formula and solve for c:
[tex]c = \sqrt{a^2 + b^2 - 2(a)(b)(\cos A)}[/tex]
[tex]c = \sqrt{20^2 + 20^2 - 2(20)(20)(\cos 120)}[/tex]
[tex]c = \sqrt{400 + 400 - 2(20)(20)(\cos 120)}[/tex]
[tex]c = \sqrt{800 - 2(20)(20)(\cos 120)}[/tex]
[tex]c = \sqrt{800 - 2(400)(\cos 120)}[/tex]
[tex]c = \sqrt{800 - 800(\cos 120)}[/tex]
[tex]c = \sqrt{800 - (-400)}[/tex]
[tex]c = \sqrt{1200}[/tex]
[tex]c = 20\sqrt{3}[/tex]
[tex]c = 34.641016[/tex]
[tex]c = 34.64[/tex]
We now have our answer, which is 34.64 and that is C.
