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Find the missing length (trig)

  1. Feb 26, 2013 #1
    Am I doing this correctly.

    VEa0He3.png

    [tex]x \tan=\frac{183}{\tan 30}=317ft[/tex]

    Also if it were the other way around and I needed to find the height but I already had the length would it just be

    [tex]h \tan=\frac{x}{\tan 60}=hft[/tex]
     
  2. jcsd
  3. Feb 26, 2013 #2

    jbunniii

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    I'm not sure what the notation ##x \tan## and ##h \tan## means.

    If ##h## refers to the height of the triangle (currently labeled 183 ft), then both of the following are true:
    $$\tan(60) = \frac{x}{h}$$
    and
    $$\tan(30) = \frac{h}{x}$$
    So if you know ##x## but not ##h##, then you can find ##h## by either
    $$h = \frac{x}{\tan(60)}$$
    or
    $$h = x\tan(30)$$
    And if you know ##h## but not ##x##, then you can find ##x## by either
    $$x = h \tan(60)$$
    or
    $$x = \frac{h}{\tan(30)}$$
     
  4. Feb 26, 2013 #3
    Thanks. I have 1 more question if you wouldn't mind confirming my answer. Just so I don't make another thread.

    A ladder is leaning against a wall. The foot of the ladder is 6.25 feet from the wall.
    The ladder makes an angle of 74.5° with the level ground. How high on the wall does the ladder
    reach? Round the answer to the nearest tenth of a foot.

    After working out the remaining angle being 15.5° I then have:

    [tex]x \tan=\frac{6.25}{\tan 15.5}=23ft[/tex]
     
  5. Feb 26, 2013 #4

    jbunniii

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    Yes, it's correct, except again I'm not sure why you wrote "##x \tan##" instead of just ##x##.

    By the way, homework and homework-like questions should go in the homework forums.
     
  6. Feb 26, 2013 #5
    x tan is just the notation they use in this book I'm learning from. It's not really a homework question I'm an independant learner and this book doesn't have the answers in the back so just wanted someone to check I was doing these correctly.

    Thanks!
     
  7. Feb 26, 2013 #6

    HallsofIvy

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    Are you sure they are not writing something like "x tan(60)" where "x" is the length of the "opposite side" to get the "near side"?
     
  8. Feb 26, 2013 #7
    Nope, the side is just labled as [tex]x[/tex] and then it just says

    [tex]x\tan= ...[/tex]
     
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