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Math Help - "Understand Trigonometry" problem

  1. #1
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    "Understand Trigonometry" problem

    I am (slowly) working my way through "Teach Yourself: Understand Trigonometry" by Hugh Neill and already I've encountered a problem which has me stumped.

    Exercise 2.3, problem 4:

    PQRS is a rectangle. A semicircle drawn with PQ as diameter cuts RS at A and B. The length PQ is 10cm, and angle BQP is 30 degrees. Calculate the length PS.

    As I'm still working my way through some basic material from geometry I'm sure I'm missing something really obvious. I've sketched what I think the set-up should be:

    "Understand Trigonometry" problem-exercise2.3.4.jpg

    and I'm thinking solving it has something to do with the geometry of a trapezoid but I'm just hitting walls! I should also point out that it's only in the second chapter of the book and so the problem must be solved using only basic rules of sine, cosine and tangent (SOHCAHTOA).

    Help?!?
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  2. #2
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    Re: "Understand Trigonometry" problem

    Join PB. Now angle PBQ is 90 degree { angle in a semicircle}. Also angle PQB = 30 degree given.
    From right angle triangle PBQ: BQ/PQ = cos 30 . From here find BQ. Now angle BQR = 60 degree and you have just calculated BQ
    proceed to get the side QR
    OK
    Thanks from Paze
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  3. #3
    Senior Member Paze's Avatar
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    Re: "Understand Trigonometry" problem

    Hi. Along with Ibdutt's explanation, you can have a look at this: Thales' theorem - Wikipedia, the free encyclopedia

    That should shed some light on your problem and the explanation.
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  4. #4
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    Re: "Understand Trigonometry" problem

    Thanks for your help, guys. As expected, my incomplete knowledge of geometry was to blame - eagerly reviewing the chapter on circles now and everything making much more sense!
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