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Math Help - Angle of depression.

  1. #1
    Member Mr Rayon's Avatar
    Joined
    Sep 2007
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    137

    Angle of depression.

    Kath stands at the top of a vertical cliff. She sights a ship on the ocean at an angle of depression of 7 degrees. The ship moves directly away from where Kath is standing, until after it has travelled 1100 m, the angle of depression is now 5 degrees.
    a) Use the sine rule to find the direct (line of sight) distance from Kath to the ship at its second location, correct to the nearest metre.
    b) Hence or otherwise find, correct to nearest metre:
    i) the height of Kath above the ocean
    ii) the distance of the ship from the base of the cliff before it travelled the 1100 m.

    Please show any working out. I would love to see some help regarding these questions.
    Last edited by mr fantastic; June 23rd 2010 at 03:14 PM.
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  2. #2
    Super Member bigwave's Avatar
    Joined
    Nov 2009
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    honolulu
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    580

    Cool law of sines

    first by geometry get the interior angles of the triangle then use the law of sines to get the sides.
    the interior angles should be (that is if I see this correctly) are 2^o 5^o and 173^o

    since the "direct(line of sight) distance" is opposite of 173^o and 1100m is opposite of 2^o we can use the law of sines to get the distance
    now solve for x which is the distance of the line of sight
    \frac{\sin{173^o}}{x} = \frac{\sin{2^o}}{1100}

    can you get the rest of it.....
    Last edited by bigwave; June 23rd 2010 at 03:29 PM. Reason: more steps
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