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Math Help - Trigonometry problem

  1. #1
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    Trigonometry problem

    Hi all,

    I was doing the problem attached, but cannot understand what is meant by E 70 S. Can someone please help me out. the Answer should be 13.57.

    I also attached the sketch diagram.
    Attached Thumbnails Attached Thumbnails Trigonometry problem-231120121288.jpg   Trigonometry problem-1.jpg  
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  2. #2
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    Re: Trigonometry problem

    Hey aritech.

    For this problem E 70 S refers to a bearing which I think is east 70 south, or in translation a bearing of 70 degrees from either the south or east axis in either clock-wise or counter-clockwise direction.

    However, the diagram doesn't indicate that either of the above are correct.
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  3. #3
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    Re: Trigonometry problem

    Hi chiro, the diagram attached is sketched be me, so it can be incorrect. I searched on the net for bearings and i found the picture attached. The E 70 S is most probably referring to the angle between 90 and 60. But still, i don't know which is the angle of descent which will result to 13.57.
    Attached Thumbnails Attached Thumbnails Trigonometry problem-comp_quad.gif  
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  4. #4
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    Re: Trigonometry problem

    Any help please?
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  5. #5
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    Re: Trigonometry problem



    first sighting ...

    distance from the airport, d_1 = \frac{8000}{\tan(40)} \approx 9534 \, m

    second sighting ...

    distance from the airport, d_2 = \frac{5500}{\tan(35)} \approx 7855 \, m


    distance traveled parallel to the earth's surface, r = \sqrt{9534^2 + 7855^2 - 2(9534)(7855)\cos(70)} \approx 10068 \, m


    descent angle \theta = \arctan\left(\frac{8000-5500}{10068}\right) \approx 13.945^\circ = 13^\circ \, 57'

    speed \approx 231 m/s = 829.9 \, km/hr


    next time, DON'T BUMP.
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    Re: Trigonometry problem

    Thanks fro the reply
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  7. #7
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    Re: Trigonometry problem

    Hi again, I cannot understand the working 100%, so I sketched a new diagram. Is the angle of descent the one marked with the green ?? and where in the diagram is E 70 S please?

    Thanks in advance.
    Attached Thumbnails Attached Thumbnails Trigonometry problem-241120121289.jpg  
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  8. #8
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    Re: Trigonometry problem

    the descent angle is relative to the horizontal. it is formed by the change in altitude, 8000 - 5500 = 2500 m, over the distance traveled parallel to the earth's surface, 10068 m.
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