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Math Help - Sine Law Word Problems, How to get these answers?

  1. #1
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    Sine Law Word Problems, How to get these answers?

    I'm in grade 10 doing Sine Law at the moment and I need help with two questions.

    #1 "A ship leaves port and sails 18 km north. It then veers off course 30 degrees east. One hour after this change of course, the ship's instruments indicate that the vessel is 36.7km from port, as the crow flies. How far has the ship travelled since it changed course?"

    My teacher says it is 28km for the answer, I did it many times but I didn't get this answer, can someone show me the steps please?

    Here is a picture I drew on the computer from my homework sheet for Question #1



    #2 "The sides of a parallelogram measure 5 cm and 3cm. Calculate its area if diagonal AC is 7.65cm"

    My teacher says it is 8.64 cm2, but I didn't get the answer







    if you replied to my post, can you pm me please? I need help for a test soon. Thanks.
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  2. #2
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    Nope. Not 28 km.

    Show your workings so you can go in with a strong argument.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    Nope. Not 28 km.

    Show your workings so you can go in with a strong argument.

    well my teacher said it was 28 km? I got 8.67? or something like that...

    what did you get?
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  4. #4
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    Nope. Not 8.67 km.

    Show your workings so you can go in with a strong argument.

    It absolutely cannot be 8.67. It must be AT LEAST 36.7 - 18.0 = 18.7. It can be AT MOST 36.7 + 18.0 = 54.7. Why?

    Me? I managed the correct answer using two different methodologies for surety. You give it another try and SHOW YOUR WORKINGS!
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  5. #5
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    Quote Originally Posted by TKHunny View Post
    Nope. Not 8.67 km.

    Show your workings so you can go in with a strong argument.

    It absolutely cannot be 8.67. It must be AT LEAST 36.7 - 18.0 = 18.7. It can be AT MOST 36.7 + 18.0 = 54.7. Why?

    Me? I managed the correct answer using two different methodologies for surety. You give it another try and SHOW YOUR WORKINGS!
    I remember getting 54.7 when I tried it many times, but I'm pretty sure I didn't do the adding...well here was how I did mine....I did sine law because it is not right angle triangle, refer to picture on my first post to understand my steps.my final answer here is 20.3



    Also, can you help me with the second question with the parallelogram?
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  6. #6
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    Too much rounding error, but I think you have it. That much rounding error is common for rounding everything to two decimal places.

    I get B = 14.195521

    C = 15.804479

    and c = 19.990891

    Of course, since we started with only three significant digits, there are good arguments for your value and many other things in between. Personally, I think significant firgure rules are a little out-dated. There is no need to add rounding error deliberately. Besides, it always has bothered my that 1/4 is easier to judge than 3/10, but since 1/4 = 0.25 and creates another decimal place, it cannot be acceptable.

    Anyway, keep up the good work.
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  7. #7
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    Quote Originally Posted by TKHunny View Post
    Too much rounding error, but I think you have it. That much rounding error is common for rounding everything to two decimal places.

    I get B = 14.195521

    C = 15.804479

    and c = 19.990891

    Of course, since we started with only three significant digits, there are good arguments for your value and many other things in between. Personally, I think significant firgure rules are a little out-dated. There is no need to add rounding error deliberately. Besides, it always has bothered my that 1/4 is easier to judge than 3/10, but since 1/4 = 0.25 and creates another decimal place, it cannot be acceptable.

    Anyway, keep up the good work.
    well my calculator is TI-30XA, i didn't round up, I just kept the number...I guess I might have to ask my teacher...
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  8. #8
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    It would be good to decide on rounding rules. If you like one way, and your teacher likes some other way, this could go quite poorly on an exam.

    In any case, if you show your work so that it is reproducible, like you just did, it should go well.
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