# &nbsp;&nbsp;&nbsp; A kite 100ft above the ground m...

A kite 100ft above the ground moves horizontallyat a speed of 8ft/sec. At what rate is the angle between thestring and the horizontal decreasing when 200ft of string have beenlet out.

THANKS

1. Using Pythagoras theorem in right angled triangle ABC ,BC=Ö2002-1002=173.2ft
Now angle A is given by tan(A)= 173.2/100=1.732 that isangle A = 600. Thus the angle which the 200ft of stringmakes with the horizontal is (90-60)=30degrees. And thereforethe angle is changed from 90 to 30 thus it has got a change of60 degrees.
Now the kite travels a distance of 173.2ft in(173.2ft)/(8ft/s)=21.6s
Hence the rate of change of angle is (60/21.7)=2.77degrees per second.
*I am not sure about the solution but i feel that this must bethe procedure of solving.
2. In the right angled triangle ABC , tanq=100/x or cotq=x/100
Now using pythagoras theorem AB=
Thus
or
The kite is moving with a speed of 8ft/s thus it covers adistance of 173.2ft in time given by 173.2/8 s=21.6s
Hence the rate of change of angle is
(minus sign as angle is decreazsing)

3.                                       x

sorry i didn't draw in the earlier post but that's what my profhad.