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Math Help - trig word problem help

  1. #1
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    trig word problem help

    The problem is attached to the post
    I really dont know how to turn that into a graph
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  2. #2
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    Quote Originally Posted by triggy22 View Post
    The problem is attached to the post
    I really dont know how to turn that into a graph
    to a):
    Use the definition of Cosine:

    \dfrac wd = \cos(x)~\implies~d=\dfrac w{\cos(x)} = w\cdot \sec(x)

    to b):
    \min(x) = 0~\implies~d = w

    If P = L then \max(x) = \arctan\left(\dfrac{2w}w\right)=\arctan(2) \approx 1.1071...

    to c)
    If x = 0 then d = w
    if x = \arctan(2) then d = \sqrt{(2w)^2+w^2}=w\sqrt{5}

    Therefore w\leq d \leq w\sqrt{5}

    to d)
    I'll leave this part for you.

    to e):
    That depends on how fast the life-guard is able to run or to swim.
    Maxiumum way to run = 3w
    Maximum way to swim = w\sqrt{5}

    Let v_r denote the running speed and v_s the swimming speed then the lifeguard will swim if

    \dfrac{w\sqrt{5}}{v_s} < \dfrac{3w}{v_r}
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