Respuesta :
We are given : Distance of the swing = 100 feet.
Distance of slide = 80 feet.
Angle between swing and slide = 30 degrees.
We need to find the distance between the swing and the slide.
Distance of swing, distance of slide and distance between the swing and the slide form a triangle.
We can apply cosine law to find the distance between the swing and the slide.
c^2 = a^2 +b^2 - 2ab cos C
c^2 = 100^2 +80^2 - 2(100)(80) cos 30°
c^2 = 10000 + 6400 -2* 8000 [tex](\frac{\sqrt{3}} 2)}[/tex]
c^2 = 16400 - 8000[tex]\sqrt{3}[/tex]
c^2 = 16400 - 13856
c^2 = 2544
[tex]c =\sqrt{2544}[/tex]
c= 50.44
c = 50 feet approximately.
