Tree-gonometry!

So here you are, at the end of your studies of Trigonometry. Take some time to think of all the new things you have learned – you have all covered so much, and you should be proud of what you have achieved.

Now it is time to get the reward your efforts have earned – this week is test week (both ODT & Trigonometry!). You know what skills we have practiced through our tests this year, and you need to be prepared for the same structure again – but you should be planning how you will best make use of your time, to demonstrate your knowledge. Remember what we have spoken about regarding “owning your test” – it belongs to you, and at the end it shows what you can do. Since it is all about you, it is yours to do with what you want to. Choose your own path!

Some of the things you have learnt are how trigonometry can be applied to non-perpendicular triangles (the sine & cosine rules).

These rules can be used with right-angled triangles as well, but are probably more difficult to use! Some of you are finding the Ambiguous case of the sine rule difficult to get your heads around, so here is a video that may help you understand:

There is another good video here – watch them both until you are sure you know how to handle these problems.

The next major skill you have to master is the trigonometry of navigation – bearings and vector resolution, and the relationship between global navigation and spherical trigonometry. I have found four videos that illustrate these ideas (1, 2, 3, 4).

You will also want to master the unit circle – ensure that you know how Sine, Cosine & Tangent all relate to parts of the Unit Circle, and identify which are positive in which quadrant.

There is a previous post on CyberChalky that goes into much greater detail – you may want to check it out.

Finally, the project that you are all working on – to use trigonometry to determine the height of an object (be it a tree, light tower or goal post). Your task was to use at least two different techniques (such as direct calculation, known distance, similar triangles, the “scout” tricks and technological tricks such as Iphone apps) to accurately find that height. There are three parts of the assessment:

  1. The mathematical aspect: this includes explaining how the technique is applied, and the correct mathematical workings.
  2. The accuracy aspect: taking into account the uncertainty in the physical measurement and calculating an appropriate range for answers
  3. Reconciliation aspect: combining your answers from the different techniques in a meaningful way to justify a reasonable final answer.

You are expected to present your work as a coherent and well organised whole – this project assesses you ability to work mathematically as well as deal with real world measurements.

The final due date for this task is the 15th of August. A rubric will be posted here shortly.

See you in class!

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41 Comments on “Tree-gonometry!”

  1. Manar Says:

    Hey sir, in the Reconciliation aspect, when you mentioned ” justify one final answer”, what did you mean by that… And is it alright if I can represent my 3 measurements of the tree in poster format?

    • CyberChalky Says:

      Manar,

      By justify one final answer I mean you should combine your three measurements into a single more accurate measurement; just like you do in a science experiment.

      • Manar Says:

        So could i add all three measurements or something.. and I dont get what it means by the “range”. I have all three measurements but dont know how i could combine them or finding a range??

        • CyberChalky Says:

          OK Manar,

          Have you tried googling “definition: range” or something similar? Range is the numerical “distance” between the maximum & minimum possible values for a measurement. So for example: if my minimum value for height is 12 and my maximum is 15, my range would be (15 – 12) = 3.

  2. Bernice Says:

    Hi Sir,

    For the second task in maths online, it’s really confusing me and I’m not sure how to do it properly. I’ve watched the video several times and I still don’t get it. Is it possible for you to explain it to us on Monday? Thanks.

    • ithinkitsme Says:

      Sir, I second this. I really have no clue how to do it, and would also appreciate help.
      And, about this maths assignment. I have used six different techniques, each with a different smallest and largest possible height, and have graphed it like you said. but there is no common range between every technique, it’s too sporadic. So how would you suggest I come to a final answer? Use this graphing to the best it can be used, or should i forget it and find an average between all the possible heights?

    • Tia C. Says:

      Sir, I second this. I really have no clue how to do it, and would also appreciate help.
      And, about this maths assignment. I have used six different techniques, each with a different smallest and largest possible height, and have graphed it like you said. but there is no common range between every technique, it’s too sporadic. So how would you suggest I come to a final answer? Use this graphing to the best it can be used, or should i forget it and find an average between all the possible heights?

    • Ellayne Garcia Says:

      I don’t get it as well. It seems that I have to watch the other videos before I can fully understand it.

      Also, is it included in the maths test Sir? I hope not.

    • CyberChalky Says:

      I can, but perhaps you could also ask a question here on the blog?

  3. Andrea Says:

    Sir this assignment is doing my head in. So i’m going to make a draft to show you Monday, and could you just check it out to see if I’m on the right track. So I guess I’m asking for an extension…

  4. Manar Says:

    Yeah I agree with Andrea, could I possibly do the same thing and show you sir?

  5. Prathu Khairnar Says:

    hey sir,

    i have a question for finding the area of the triangle.

    do we have to use cosine and sine rules to find the answer? i mean is there any easier or shorter way?

    i find those questions too long is there anyway to minimise the problem?

    • CyberChalky Says:

      Hi Prathu,

      I’m guessing you’ve not read the section in your textbook? Area = 1/2 * b * c * sin A

      • Prathu Khairnar Says:

        yes i read it, but that only implies on a trignale with 2 given sides, and a angle

        what happens when there are two given angles and only one side?…

        and also what happens when there is 2 given sides and one inlcuding angle, but the angle in on the other side, (a triangle which could only be solved by sine rule, and not a cosine rule)

        and i dont understand herons formula either?… What exaclty is “S” in the text book?

      • Hao Says:

        According to the book, S is just 1/2(a+b+c)
        But what do you do if teh triangle only has 2 sides. :/

      • Hao Says:

        Wait, nvm. Dont worry about that last line that I wrote. -_-

      • Prathu Khairnar Says:

        hey sir,
        i am redoing my assignment as u suggested… just one question, am i allowed to do three-dimensional trigonometry problems?

      • Prathu Khairnar Says:

        ummm… sir i need extension of just more day.. plz

  6. Tia Says:

    Hey Sir, would I be able to have an extension too please? I have completed almost everything, I’m just stuck on the final results (compiling the result of every technique into a final answer), which I’m hoping you can help me with tomorrow.

  7. Nur Zahidah Says:

    Mr Gritching, I just found out that the project was due yesterday so now I’m just rushing and trying to get everything completed.
    I’ve done my 2 techniques.. well its like 3-4 techniques and some are combined. Could you please tell me how to do that plus minus thing (I seriously forgot what it’s called) It’s the formula used to show the accuracy and inaccuracy of measurements.

    I really hope I can get it done by tomorow.

    🙂

    • Nur Zahidah Says:

      Due today i mean **

    • CyberChalky Says:

      Hi Zahidah,

      It’s called “measurement uncertainty” or “measurement error”. It’s a bit hard to explain on the blog, but try these video links:

      [video src="http://reesfilms.com/drupal/movie.php?filename=Measure1_clip2.mov.ff.flv" /]

  8. Manar Says:

    Hello sir,
    i just have one question to ask. I have completed 2 methods now so i might need 1 or 2 more, so what is the difference between the shadow method and the similiar triangles method explained in the textbook??

  9. Jana Says:

    Hey Sir
    I’m pretty much finished for the most part, the only problem I keep having is with the stuff you put up on the board.

    So far, I’ve got
    tan26(x+10) = xtan21

    …not that that will make any sense.
    Is there any chance you could recall the example you put on the board or a similar one?
    I just keep having issues with it and get lost in how to re-arrange the whole thing.

    Thanks..

    • CyberChalky Says:

      Expand the bracket:
      xtan26 + 10tan26 = xtan21
      put the x terms on the same side
      10tan26 = xtan21 – xtan26
      Factorise by removing the common factor “x” from the right hand side
      10tan26 = x(tan21 – tan26)
      Divde through by the bracket
      10tan26/(tan21-tan26) = x

      Finished. Although I think you have a mistake in that it should be tan21(x+10) =xtan26 at the start….

      • Jana Says:

        thank you!!!
        the working out i had on my page was way off.
        yeah that was a mistake. i think i’ve got it now, thanks again!

  10. Chantelle Says:

    Hey sir,
    I don’t think I will be able to finish the assignment by tomorrow, is it possible to have an extension until Wednesday?


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