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Math Help - I don't understand Trigonometry

  1. #1
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    Exclamation I don't understand Trigonometry

    A new tower has been built in the Docklands area of Melbourne, claiming, at 660 m to be the tallest building in the world. Two students at different schools worked together to check the builder's claims.

    From a site in the middle of her school oval, Jenny found that the tower was at a bearing of 040░ T, and the top of the tower had an angle of elevation of 5░ 30'.

    From a site in the middle of the oval next to his school, Michael found that the tower was at a bearing of 081░ 30' T, and the top of the tower had an angle of elevation of 6░ 15'.

    As the two students could not see each other vusually, they each used large scale maps of Melbourne to determine the distance between the two measuring sites, and the bearing of one site from the other.

    Jenny determined that Michael's site was at a bearing of 342░ 30' T from her site.

    Michael determined that Jenny's site was at a bearing of 162░ 30' T from his site.

    They both agreed that the two sites were separated by 4640 metres. Both students assumed that their sites were level with the base of the tower.

    (a) Draw a scale diagram of the situation as either Jenny or Michael would have drawn it, using the baseline length, the site bearing data and the tower bearing data. Mark in all known angles and distances on this scale diagram.
    Clearly show the scale used.

    (b) What is the real distance, as determined from your scale diagram:
    (i) from Michael's site to the Tower
    (ii) from Jenny's site to the Tower




    There are other questions to this activity but I think I need to know the above to complete those. If I still don't understand how to do them I will post my other questions below. All help will be appreciated!
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  2. #2
    MHF Contributor

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    Have you drawn a picture? Ignoring the height for the moment, you should be get a triangle with vertices at the building, Jenny and Michael. From the bearings you know all three angles in the triangle and you know one side (the distance from Michael to Jenny). Use either the sine law or cosine law to find the lengths of the other two sides (from Jenny to the building and from Michael to the building). Knowing those distances, use the angle of elevation and the definition of the "tangent" function to find the "opposite side" of a right triangle: the height of the building.
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