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Secondary education

Please help me - maths

12 replies

Mathshelpme · 11/05/2021 18:08

If anyone can help me understand this, I’d be grateful!

Please help me - maths
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TeenMinusTests · 11/05/2021 18:42

Ooh that looks tricky. I'm a bit rusty on this. Is it A level or GCSE (which would give an idea of how complicated to get).

You should be able to find diagonals on rectangles using Pythagoras.
You should be able to find length BE by Pythagoras with first calculating BG
Your trapezium is right angled so you can find the length of BC also by pythag (using AG and difference of AB and GC)
By now you know the 3 sides of the triangle so can use one of the trig rules to find the desired angle? (a2=B2+C^2-2bccosA?)

Seems a bit complicated for only 9 marks though, so I may well be missing an easier method.

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Mathshelpme · 11/05/2021 18:43

It’s additional maths, so I think a stepping stone between GCSE and A level.
Thank you for the starting point though! Going to have a good look at this again with your advice now!

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TeenMinusTests · 11/05/2021 18:48

If you have any straws or similar at home, make a 3D model to help you visualise it. (We used to use magnetix or knex)
You need to spot the planes with lengths you know and/or right angles.

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Mathshelpme · 11/05/2021 18:50

Thank you! Straws on the shopping list!
Just worked out BG and BE so en-route!

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Wobblypig · 11/05/2021 21:39

Key lies in fact that all other faces are rectangles.

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Whythesadface · 11/05/2021 21:58

If you extend GC and call it NC...
So 8.4 - 6.2. gives you NC 2,2
Your Triangle is BCN... 2,5 by 2,2 ,,, BC 3,33 is the length,,,

Triangle EGC is the next one
So 6.2 - 3.7 EC is 7,2

You now have ECB measurements and can work this out,

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Mathshelpme · 11/05/2021 22:20

Thank you everyone! I think(?) we’ve done it and got 125 degrees...

I hope we’ve done it 😬

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woodlands01 · 11/05/2021 22:48

Agreed! Maths teacher here - that is a GOOD question.

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woodlands01 · 11/05/2021 22:51

I think the tough bit about that question is that you have to visualise EB as the longest diagonal of the cuboid & apply Pythagoras in 3D. Once that is clear in your head then it's actually ok.

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TeenMinusTests · 12/05/2021 05:36

Glad you're sorted.
Visualising the middle of a 3D object is hard.
(Also glad I haven't forgotten everything I ever knew.)

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FlattestWhite · 12/05/2021 10:05

What looks like the hard bit to me is how to extend the bottom diagonal EC, so that you can make a right angled triangle to find the 3D diagonal. I was thinking that the difference between the top and bottom of the trapezium (the 8.4-6.2) would both extend GC to allow you to find BC, but then it would also be like the radius of a circle, to mean that EC also has to be extended by this same amount to find the bottom of a right angled triangle with the perpendicular height. Then pythagoras to find the long diagonal. Finally cosine rule.

That might be what someone has said but I'm not sure if there was an easier way to find that long diagonal without extending the base diagonal.

K-nex sounds like a great idea, I hate trying to explain things in 3D to people when I find it hard to visualise!

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FlattestWhite · 12/05/2021 10:08

oh, actually I see how you're all finding EB, you're using the diagonal of the 'back', and then the depth, that seems easier actually. It's hard to picture which ones are rectangles vs trapeziums from the 2D picture.

Nice question, yes.

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