Like Tree19Likes

Up to a trigonometry puzzle ?

Reply
Page 3 of 3 FirstFirst 1 2 3
  1. #21

    Join Date
    May 2006
    Location
    Pampanga, Philippines
    Posts
    20,189
    Quote Originally Posted by jrkob
    Yes correct. I'm not a mind reader but it seems to me that perhaps using the protractor is an intermediate step before they learn cos/sin/tan. After all, an angle as a measure of π is nothing more than the inverse of a cos/sin.
    @hullexile @mrgoodkat here's the full assessment with Billy the Goat.

    For c, I'm finding 82.2 meters, if someone is doing the work, either using standard radians or a protractor, let me know what you find.

    Attachment 79020
    I wondered what age the kids are?

  2. #22

    Join Date
    Feb 2015
    Location
    Hong-Kong
    Posts
    5,503
    Quote Originally Posted by hullexile
    I wondered what age the kids are?
    It's year 8 at AISHK, kids are 14. Would this be of similar level in the UK ?
    I showed the assessment to my sister back home and she said over there they wouldn't give this assessment at this age, too early. But then our education system over there has become a fringging joke.
    hannah01 likes this.

  3. #23

    Join Date
    Sep 2017
    Posts
    335

    I hate(d) trigonometry with all my heart at school. Now, WHAT is this? I was thinking "let me save it for my kids that will exist in the un-calculated distant future" . But nay, I don't want to pre-spoil my mood.


  4. #24

    Join Date
    May 2006
    Location
    Pampanga, Philippines
    Posts
    20,189
    Quote Originally Posted by jrkob
    It's year 8 at AISHK, kids are 14. Would this be of similar level in the UK ?
    I showed the assessment to my sister back home and she said over there they wouldn't give this assessment at this age, too early. But then our education system over there has become a fringging joke.
    Not sure on UK because when my kids were there they were either too young or too old.

    Just checked here and in grade 9 there is "advanced algebra and trigonometry". She is grade 7 now. (But she is on a special government STEM scheme so not sure if that is standard).
    jrkob and nivantj like this.

  5. #25

    Join Date
    Jan 2018
    Posts
    633
    Quote Originally Posted by jrkob
    @Viktri the mistake that praetorian is making is assuming it's a square. It's not a square, it's a rectangle.
    The teacher gave a short explanation of how she's expecting the kids to look at this without knowledge of sin/cos/tan.
    BUT... have to use a x, so to me it's a "dirty" solution. But still much better than assuming the square fits into the circle.

    Here goes. First, a drawing.



    Area of the big circle: 3.14 x 4^2 = 50.24

    You measure the angle of the big slice of cheese and find... 81 degrees.
    Area of the big slice of cheese: 81/360 x 50.24= 11.30.
    Using pythagoras: alpha = sqrt(7)
    Area of the triangle inside the big slice of cheese: 3 x sqrt(7) = 7.94
    Area of the arc on top of the slice of cheese: 11.30 - 7.94 = 3.36
    The protractor is not bad exercise I think - since it is a real world problem - but if we (adults) use the triangle with a side 3, a side 4, and an angle that is 90 degrees it follows that the angle we need is 2*41.41=82.82 degrees (not 81).

    But the biggest mistake was that the unit in the original problem is meters - not centimeters.

    https://www.calculator.net/triangle-calculator.html
    jrkob likes this.

  6. #26

    Join Date
    Dec 2002
    Location
    ???
    Posts
    27,389

    This is a classic example of something that sparks viral headlines ... "How many investment bankers does it take to solve a Y8 maths problem". Bonus points if you can also figure out how to screw in a lightbulb and walk and chew gum at the same time.

    (Sorry, nothing productive to add here .... I gave up on trying to understand my kid's homework - even in subjects I studied at Uni!)

    Skyhook likes this.

  7. #27

    Join Date
    May 2006
    Location
    Pampanga, Philippines
    Posts
    20,189
    Quote Originally Posted by shri
    (Sorry, nothing productive to add here .... I gave up on trying to understand my kid's homework - even in subjects I studied at Uni!)
    Then you get some old farts saying the questions are so much easier now than they were in their day. I can only assume they have not been helping kids with their homework.
    shri likes this.

  8. #28

    Join Date
    Aug 2011
    Location
    HK
    Posts
    1,762

    I was thinking this should be solved along the lines of a calculus question. The limit of the formula of area of a circle as r moves from 4 to 3


  9. #29

    Join Date
    May 2019
    Posts
    3
    Quote Originally Posted by jrkob
    Yes correct. I'm not a mind reader but it seems to me that perhaps using the protractor is an intermediate step before they learn cos/sin/tan. After all, an angle as a measure of π is nothing more than the inverse of a cos/sin.
    @hullexile @mrgoodkat here's the full assessment with Billy the Goat.

    For c, I'm finding 82.2 meters, if someone is doing the work, either using standard radians or a protractor, let me know what you find.

    You’ll have another problem once the rope goes beyond 5m (standard 3x4x5 right angled triangle) because of the grazeable area inhibited by the wall, so you need another circle from the edge of the walls.

  10. #30
    tck
    tck is offline

    Join Date
    Jul 2015
    Posts
    108

    We have a traingle with side lengths 3, sqrt(7), and hypotenuse 4, but i can't figure out how to find the angle without law of sin to calculate the segment area blocked off by the wall?

    I cheated anyway and just used law of sin to find that interior 82.8 angle. But was there another way to figure that out?

    Anyway, after doing that and plugging and chugging.

    Area of Circle = 4^2*pi

    Area of segment blocked off by wall = Area of Sector - Area of triangle from center post to ends of the 8 meter wall

    Area of sector = (82.8/360)*16pi

    Area of Triangle = 3*sqrt(7)
    Total area grazable given at a rope of 4 meter length ~ 46.6 square meters.

    This makes some intuitive sense as if you just assume triangles, 16 pi - a triangle that looks roughly 3 square meters large about 47 square meters.


Reply
Page 3 of 3 FirstFirst 1 2 3