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Math Help - Trig word problem

  1. #1
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    Trig word problem

    From a balloon the angle of depression of a ground marker is 35 degrees. From a point 200m higher the angle of depression is 54 degrees. Find the distance from the marker to the point on the ground directly beneath the balloon.

    How do you solve this?
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  2. #2
    Super Member bigwave's Avatar
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    Cool

    there are several ways to solve this

    one is find the distance from the marker to the balloon which would be an hypotenuse then you find the base which the distance from the marker to the spot directly under the balloon.

    some useful tools here is the law of sine's and the Pythagoran therom

    do you want to see the steps to do this
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  3. #3
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    Could you do this using trigonometric ratios? cause I think my teacher expects that.
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  4. #4
    Super Member bigwave's Avatar
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    Cool

    Quote Originally Posted by sinjid9 View Post
    Could you do this using trigonometric ratios? cause I think my teacher expects that.
    Law of Sines is one the trigonometric ratio's you can use

     <br />
\frac{\sin{\alpha}}{a} <br />
= \frac{\sin{\beta}}{\beta} <br />
= \frac{\sin{\gamma}}{\gamma}<br />

    again, several ways to solve this but
    do you know how to use the law of sines with this
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  5. #5
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    I know how to use it but don't you need a angle and the side length opposite to it?
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  6. #6
    Super Member bigwave's Avatar
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    Quote Originally Posted by sinjid9 View Post
    I know how to use it but don't you need a angle and the side length opposite to it?
    other angles are easily derived, from geometric theroms. the interior angles are 36^o, 126^o and 18^o
    Last edited by bigwave; May 17th 2010 at 06:45 PM.
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  7. #7
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    I got around 295m but the sheet says its 285m...
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  8. #8
    Super Member bigwave's Avatar
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    Cool

    actually I got 307.89 which isn't the given answer either.

    \frac{\sin{18^o}}{200m} = \frac{\sin{126^o}}{\gamma}<br />
\Rightarrow \gamma = 523.61m

    \Rightarrow \left(523.61\right) \cos{54^o} = \beta = 307.89
    Last edited by bigwave; May 17th 2010 at 07:12 PM.
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