Help me??

Kyle is pulled back on a swing so that the rope forms an angle of 35° with the vertical. The distance from the top of the swing set directly to the ground is 11 feet. Find Kyle’s height off the ground, x, when he is in the pulled-back position. Round the answer to the nearest hundredth.

Question

Help me??

Kyle is pulled back on a swing so that the rope forms an angle of 35° with the vertical. The distance from the top of the swing set directly to the ground is 11 feet. Find Kyle’s height off the ground, x, when he is in the pulled-back position. Round the answer to the nearest hundredth.

anonymous · Answer

attachment

anonymous · Answer

@ZeHanz

anonymous · Answer

top of the swing from ground=11ft
from the figure height of the swing chair above the ground=2ft
length of the swing=11 - 2 =9ft
now the swing makes an arc of 35 degree
lenght of the arc=$$(35/360)*(2*\pi*9)$$=5.4977 ft
consider this arc as a straight line

zehanz · Answer

I get another answer: swing length is 9 ft: agreed.
cos(35 deg) = vertical edge of triangle/9, so the vertical edge is 9*cos(35 deg).
x = 11 - 9*cos(35 deg) = 3.63 ft.

anonymous · Answer

@ZeHanz You're right, but could you break it down for me please?

zehanz · Answer

See the attached image.
YOu have to know what the length of CD is.
In triangle EDC, cos(35deg)= CD/EC = CD/9.

So CD/9=cos(35deg), this means: CD = 9cos(35deg).

Now x = AD = AC - CD = 11 - 9cos(35deg) = 3.63 ft.