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Math Help - Stuck on something I have to finish today...

  1. #1
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    Stuck on something I have to finish today...

    I have a final assignment for my one precalc college class due today, and the one part of it is just killing me, and I can't figure it out. This is a screen cap of the problem:

    http://i276.photobucket.com/albums/k...os/problem.jpg

    I don't know how to solve, well, any of that. Word problems just drive me crazy. >_< I don't even know how to get started on any of that. If some one could at least get me on the right track for those problems, that'd be great.
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  2. #2
    MHF Contributor

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    Well, (a) is almost trivial. The screen goes from 0 to 60. For a person setting where y= 10. the top of the screen is 60- 10= 50 feet above and the bottom of the screen is 10 feet below.

    (b) Draw a line from the person at (30, 10) perpendicular to the screen. You now have two right angles, one with legs of length 30 (to the screen) and 50 (to the top of the screen). With \theta_1 the angle the top of the screen makes with the horizontal, tan(\theta)= 50/30. The other right triangle has legs of length 30 (to the screen) and 10 (to the bottom of the screen). With \theta_2 the angle the bottom of the screen makes with the horizontal, tan(\theta_2)= \frac{10}{30}. Find those two angles (use arctan on a calculator) and add them to find the full angle.

    (c) Repeat the same computations as in (a) and (b) for general "x". Since the line is y= x- 20 a viewer at (x,y)= (x, x- 20), being x-20 feet high, has distance to the bottom of the screen x-20 and distance to the top of the screen 60- (x- 20)= 80- x. Now you have a right triangle with "near side" of length x a "opposite side" x- 20 and another with "near side" x and "opposite side 80- x. Each angle will be an arctangent and the entire angle will be their sum.

    (d) Set the formula you got in (c) equal to 60 and solve for x. Be sure your calculator is in radian mode.

    (e) Set the derivative of the formula in (c) equal to 0 and solve for x.
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  3. #3
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    Thank you so much!
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