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Math Help - sine law question

  1. #1
    Senior Member euclid2's Avatar
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    sine law question

    St. Thomas Aquinas High School in Kenora has a triangular shaped window in the main hall. The angle at the top of the window is 800 and the angles at the bottom are each 500. If the sides of the window are 3.15 m long, how wide is the window at the bottom? Show your calculations.
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    Quote Originally Posted by euclid2 View Post
    St. Thomas Aquinas High School in Kenora has a triangular shaped window in the main hall. The angle at the top of the window is 800 and the angles at the bottom are each 500. If the sides of the window are 3.15 m long, how wide is the window at the bottom? Show your calculations.
    I'm guessing that an angle of 800 and 500 means 80 degrees and 50 degrees respectively. It doesn't help things when your notation is poor.

    Have you drawn a simple diagram? The sine rule is the wrong tool for the job. The cosine rule is what's required:

    x^2 = 3.15^2 + 3.15^2 - 2(3.15)(3.15) \cos(80^o).

    Although you should see from your simple diagram that there's another way of doing it using right angle triangles ...... (use this method to confirm your answer).
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    Senior Member euclid2's Avatar
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    Thanks, makes sense.
    But how can you use right angle triangles without a 90 degree angle?
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    Quote Originally Posted by mr fantastic View Post
    I'm guessing that an angle of 800 and 500 means 80 degrees and 50 degrees respectively. It doesn't help things when your notation is poor.

    Have you drawn a simple diagram? The sine rule is the wrong tool for the job. The cosine rule is what's required:

    x^2 = 3.15^2 + 3.15^2 - 2(3.15)(3.15) \cos(80^o).

    Although you should see from your simple diagram that there's another way of doing it using right angle triangles ...... (use this method to confirm your answer).
    Actually I was a bit quick to condemn the sine rule in this question ......

    \frac{x}{\sin 80^o} = \frac{3.15}{\sin 50^o} \Rightarrow x = \, ......
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    Quote Originally Posted by euclid2 View Post
    Thanks, makes sense.
    But how can you use right angle triangles without a 90 degree angle?
    You have an isosceles triangle. Drop a perpendicular from the 80 degree angle to the base ........
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    Senior Member euclid2's Avatar
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    oh ok, thanks.
    answers are similar but obviously not the same. 4.2?
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    Quote Originally Posted by euclid2 View Post
    oh ok, thanks.
    answers are similar but obviously not the same. 4.2?
    No. You're probably doing the calculation in stages and rounding (prematurely) at each stage. Premature rounding causes a butterfly effect and can significantly effect the accuracy of your final answer.
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    Senior Member euclid2's Avatar
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    you said x/sin80=3.15/sin50
    therefore x=3.15sin80/sin50
    x=4.2m
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    Quote Originally Posted by euclid2 View Post
    you said x/sin80=3.15/sin50
    therefore x=3.15sin80/sin50
    x=4.2m
    The answer is NOT 4.2 m.

    But if you insist that it is, I'm not going to waste my time arguing about it.
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    Senior Member euclid2's Avatar
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    I don't intend on wasting either of our time arguing. You get easy posts out of it, as well as the good feeling of helping someone. I showed my calculations with a hope that you would tell me what I did wrong.
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    Quote Originally Posted by euclid2 View Post
    I don't intend on wasting either of our time arguing. You get easy posts out of it, as well as the good feeling of helping someone. I showed my calculations with a hope that you would tell me what I did wrong.
    1. I don't look for 'easy posts'. It's not a competition. I'm sorry to see that you seem to think that it is. In fact, for various reasons I nearly left your original question for someone else to answer.

    2. x = 3.15 sin80/sin50 is correct. If it was wrong, I would have said so.

    3. The numerical value of 4.2 is incorrect. I said it was incorrect. I suggested why it was incorrect. Under the present circumstances you cannot possibly expect me to see the mistake(s) you're making that have lead you to this particular incorrect numerical answer. Clearly you're either using your calculator incorrectly, consistently misreading its display or don't know how to correctly round to one decimal place.

    For the record, the answer, correct to two decimal places, is 4.05 m.
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    Senior Member euclid2's Avatar
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    Ok, well then I don't know how to round because I certainly know how to use my calculator. Thanks for taking the time to help
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    Quote Originally Posted by euclid2 View Post
    you said x/sin80=3.15/sin50
    therefore x=3.15sin80/sin50
    x=4.2m
    better recheck that calculation ... x = 4.05
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