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Math Help - Finding the length

  1. #1
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    Question Finding the length

    I have an issue with this question that why in the solution 2 is multiplied to the radius of 6400.


    The question is....

    Q)the angle subtended by the earth at the eye of the spaceman landed on the moon is 1 degree 54 minute.The radius of earth is 6400 km.Find the approx distance b/w the moon and the earth.

    Solution:

    r=L/Theta
    r=2*6400/0.033155

    r=386065.45 km Ans
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  2. #2
    MHF Contributor
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    Hi

    Since L is much bigger than r, we have \tan \frac{\theta}{2} \approx \frac{r}{L}

    Since the angle is very low, we have \tan \frac{\theta}{2} \approx \frac{\theta}{2}

    Therefore \frac{\theta}{2} \approx \frac{r}{L}
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  3. #3
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    cant understand u
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  4. #4
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    Hello, haftakhan!

    Did you make a sketch?


    Q) The angle subtended by the earth at the eye of the spaceman
    on the moon is 1 degree 54 minutes. The radius of earth is 6400 km.
    Find the approx distance b/w the moon and the earth.
    Code:
                                          *
                                  *   *   | - *
                          *         *     |R    *
                  *                *      |      *
          o        @               *      *      *
                  *                *      |      *
                          *         *     |R   *
                                  *   *   |   *
                                          *

    Do you see why we use 2R ?


    BTW, their answer is off.

    1 degree, 54 minutes .= .1.9 degrees.

    . . And 1.9 degrees = 0.033161256 radians.

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