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erik05

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1) A wall of height 8 m stands parallel to and 27 m from a tall building. A ladder with its foot on the ground is to pass over the wall and lean on the building. What angle will the shortest such ladder make with the ground? Ans: 0.58800

I think to get to the right answer, you have to end up with tanx= 2/3 and take the inverse to get 0.58800. Not quite sure how to get to that though.

2) A kite 40 m above the ground moves horizontally at the rate of 3 m/s. At what rate is the angle between the string and the horizontal decreasing when 80 m of string has been let out? Ans: 0.02 m/s

So far all I have is a triangle with a=40, b=x, c= 80 so cosØ= x/80. Taking the derivative: dx/dt= 80-sinØ dØ/dt. This was where I got stuck.

3) Two sides of a triangle are 6 and 8 metres in length. If the angle between them decreases at the rate of 0.035 rad/s, find the rate at which the area is decreasing when the angle between the sides of fixed length is [tex] \frac {\pi}{6} [/tex] ? Ans:0.727 m^2/min

Would the cosine law be involved in this to find dA/dt?

As you can see from my feeble attempts, I really suck at this. Any help with how to get the solutions would be much appreaciated. Thanks.