Maths problem

[1fast1]

2 minutes ago, Wind30 said:

thanks. Your solution is more elegant than mine. Mine was a bit convoluted. I thought most of such questions have easy solution once you get the trick. 

I think the main trick is to shift the shorter line KP to LA. From then on, it is kind of obvious. 

My daughter is still trying to solve this... 

As mentioned, the trick is to find a way to show that arctan 1/3 + arctan 1/2 = 45 deg, without trigonometry.

At that point, you try to find diagonals of squares or right isosceles triangles, which is how I came up with my solution.

Using coordinate geometry for it is a doddle, but when you're limited to the tools open to Pri sch kids, then you have to get creative.

[Ender]

7 hours ago, Wind30 said:

Can u guys solve this? No usage of sin cosine as it is primary question.

7 hours ago, Wind30 said:

 

 

Serious primary? Maybe gifted school. 

Thanks to turboflat4 solution. I also loss. 

Edited December 13, 2019 by Ender

[1fast1]

1 hour ago, Turboflat4 said:

 

I was rushing for time before, so I did a better diagram that corresponds to your original question. Hopefully, it's clearer.

You want angle KQI. Since KQ is coincident with KP, which is parallel to LA, angle KQI = angle LAI (alternate angles) = 45 degrees (angle made by diagonal AI of square ALIN with side LA). Done.

EDIT: meant "corresponding angles", not alternate angles, sorry. @Wind30

Edited December 13, 2019 by Turboflat4

[Wind30]

30 minutes ago, Turboflat4 said:

EDIT: meant "corresponding angles", not alternate angles, sorry. @Wind30

ya lar I never remember the name anyway.

But you are cheating a little if you knew the answer was 45deg. I did not calculate the answer using trigo so I could not solve it last night after thinking for 15 mins. It is rare I see a primary school question which the answer is not obvious in minutes.

Solve it this morning but my answer was much longer. I drew more lines than you.

[Wind30]

39 minutes ago, Ender said:

Serious primary? Maybe gifted school. 

Thanks to turboflat4 solution. I also loss. 

it primary school math competitions past year paper.

[Ender]

6 minutes ago, Wind30 said:

it primary school math competitions past year paper.

I see. Competition is math Olympiad or new south wale level. 

[1fast1]

36 minutes ago, Wind30 said:

ya lar I never remember the name anyway.

But you are cheating a little if you knew the answer was 45deg. I did not calculate the answer using trigo so I could not solve it last night after thinking for 15 mins. It is rare I see a primary school question which the answer is not obvious in minutes.

Solve it this morning but my answer was much longer. I drew more lines than you.

On that basis, you could argue the exam setters were also "cheating" since I'm sure they know trig and also used it. Then they figured out how to do it using elementary geometry then set the question for the kiddies. 

That's how competition questions often work. They're constructed using more involved math but designed to be creatively solved using more elementary means.

If a pri sch kid knows coordinate geometry and trig and used those, I'm sure they wouldn't deduct marks, by the way.

[Enye]

wah... when i see this type of complicated maths question which i cannot solve, i console myself that 99% of the global population won’t need to use this in their entire working lives or apply the solution in practical day to day living

🤣

[Kb27]

Sorry I have a math problem.

What's the purpose of solving this kind of complex maths question, besides bragging rights ?

Does it teach you to fit in better, or need to apply it somehow, in the real world ?

[Wind30]

26 minutes ago, Kb27 said:

Sorry I have a math problem.

What's the purpose of solving this kind of complex maths question, besides bragging rights ?

Does it teach you to fit in better, or need to apply it somehow, in the real world ?

this is something a lot people don’t understand. To me all these maths problem is training. The answer itself is not impt. There is little value doing a math problem that u knew the answer right away. I tell my kid every hard question that u cannot solve but manage to figure out in the end will increase your iq. 
to be able to figure things out instead of memorising is so impt in further education. 
As to how useful iq is in the real world, it’s up for debate. I feel at the very least it guarantee u a decent job in tech. In my field, iq is pretty impt. To be able to tell whether a new architecture will work in the first few mins is critical else weeks of effort will go to waste going down a dead end.

Edited December 13, 2019 by Wind30

[Lala81]

2 hours ago, Kb27 said:

Sorry I have a math problem.

What's the purpose of solving this kind of complex maths question, besides bragging rights ?

Does it teach you to fit in better, or need to apply it somehow, in the real world ?

The journey is more important than the answer. It's like an engineer can't learn to solve complex problems without first recognising simple problems. Never know... One day maybe your kid will be a mathematician for a living. And even if they don't, working things out logically has some benefits towards engineering or IT. Or even fixing something in the household lol. 

Without knowledge, u may not even recognise a problem, much less an opportunity. 

The problem with math is that given many Singaporeans don't actually work in engineering or create actual physical products say even a simple GPS device, we underestimate how such everyday use of math and physics relate to our world. Though they power every single device we use. 

Edited December 13, 2019 by Lala81

[Lala81]

2 hours ago, Wind30 said:

this is something a lot people don’t understand. To me all these maths problem is training. The answer itself is not impt. There is little value doing a math problem that u knew the answer right away. I tell my kid every hard question that u cannot solve but manage to figure out in the end will increase your iq. 
to be able to figure things out instead of memorising is so impt in further education. 
As to how useful iq is in the real world, it’s up for debate. I feel at the very least it guarantee u a decent job in tech. In my field, iq is pretty impt. To be able to tell whether a new architecture will work in the first few mins is critical else weeks of effort will go to waste going down a dead end.

Ha. U a systems architect? 

[Wind30]

21 minutes ago, Lala81 said:

Ha. U a systems architect? 

I do circuits design, ic chips. 

[Wind30]

Find angle x. The three sides marked are equal.

[Kusje]

On 12/13/2019 at 5:49 PM, Enye said:

wah... when i see this type of complicated maths question which i cannot solve, i console myself that 99% of the global population won’t need to use this in their entire working lives or apply the solution in practical day to day living

🤣

Nonsense leh. You can be a world class mathematician to prove that you will make a world class general and a world class pm.

[1fast1]

13 hours ago, Wind30 said:

Find angle x. The three sides marked are equal.

Ans: x = 55 degrees.

Interesting question. The key here is that 110 + 130 = 240, which allows an easy solution (otherwise it's very hard).

To see why, take a look at the first attachment. I'm working on a more general case here because it's interesting. The only assumption here (apart from the three equal sides) is that angle ABC plus angle BCD = 240 degrees (which is what we're given in the question, except I'm not even assuming a definite value for either angle).

Now, if we construct an equilateral triangle BCP, P can lie either within the quadrilateral (case 1) or outside the quadrilateral (case 2). Either way, we can show that angle APD = 180 deg, i.e. P lies on AD.

Using that (see second figure), we can immediately use basic properties of isosceles triangles to immediately work out x = 55 deg.

If you look at the third figure, which is accurately constructed (but excuse the inversion), you'll see the deep magic in the figure with two circles. Note that the collinearity of APD implies that particular angle sum of 240 degrees, and vice versa (i.e. the converse is also true).

Edited January 10, 2020 by Turboflat4

[Wildfaye29]

On 12/13/2019 at 6:21 PM, Wind30 said:

this is something a lot people don’t understand. To me all these maths problem is training. The answer itself is not impt. There is little value doing a math problem that u knew the answer right away. I tell my kid every hard question that u cannot solve but manage to figure out in the end will increase your iq. 
to be able to figure things out instead of memorising is so impt in further education. 
As to how useful iq is in the real world, it’s up for debate. I feel at the very least it guarantee u a decent job in tech. In my field, iq is pretty impt. To be able to tell whether a new architecture will work in the first few mins is critical else weeks of effort will go to waste going down a dead end.

iq is good but must have eq

[Wind30]

7 hours ago, Turboflat4 said:

Ans: x = 55 degrees.

Interesting question. The key here is that 110 + 130 = 240, which allows an easy solution (otherwise it's very hard).

To see why, take a look at the first attachment. I'm working on a more general case here because it's interesting. The only assumption here (apart from the three equal sides) is that angle ABC plus angle BCD = 240 degrees (which is what we're given in the question, except I'm not even assuming a definite value for either angle).

Now, if we construct an equilateral triangle BCP, P can lie either within the quadrilateral (case 1) or outside the quadrilateral (case 2). Either way, we can show that angle APD = 180 deg, i.e. P lies on AD.

Using that (see second figure), we can immediately use basic properties of isosceles triangles to immediately work out x = 55 deg.

If you look at the third figure, which is accurately constructed (but excuse the inversion), you'll see the deep magic in the figure with two circles. Note that the collinearity of APD implies that particular angle sum of 240 degrees, and vice versa (i.e. the converse is also true).

This solution is what my colleague gave me.

My solution is to mirror image the quadrilateral along the line AD to form a Hexagon with 6 equal sides. You should be able to prove that the angle X is half of angle 110 as that Hexagon is made up of three angles 110 and three angles 130.

I thought the question is a bit cheating as there is no solution if the angles don't add up to 240... my kid have not solve this yet after many days...

Edited January 10, 2020 by Wind30