The 5 Hardest 3D Trigonometry Questions (+1 Extra) | Grade 7-9 Maths Series | GCSE Maths Tutor

A video revising the techniques and strategies for working with 3D Trigonometry from grade 7 to grade 9 style questions. (Higher only).
Worksheet: thegcsemathstu...
This video is part of the Pythagoras & Trigonometry module in GCSE maths, see my other videos below to continue with the series.
Revision Videos:
The Entire 9-1 GCSE Maths Exam in only 2 hours!! Higher and Foundation Revision - • Everything You Need To...
Everything for a Grade 6-9 in your GCSE Maths Exam! Higher Maths Exam Revision | Edexcel AQA & OCR - • Everything for a Grade...
Pythagoras and Trigonometry Series:
All of Trigonometry in 20 Minutes!! Foundation & Higher Grades 4-9 Maths Revision | GCSE Maths Tutor - • All of Trigonometry in...
Part 1 - Pythagoras - • Pythagoras Theorem | G...
Part 2 - Trigonometry (Side Lengths) - • Trigonometry - Using S...
Part 3 - Trigonometry (Angles) - • Trigonometry - Using S...
Part 4 - Finding the Exact Values (Higher Only) - • How To Find The Exact ...
Part 5 - Sine Rule (Higher Only) - • The Sine Rule | Grade ...
Part 6 - Cosine Rule (Higher Only) - • The Cosine Rule | Grad...
Part 7 - Area of a Triangle (Higher Only) - • Area of any Triangle u...
Part 8 - Proving the Trigonometric Rules (Higher Only) - • Further Trigonometry |...
Part 9 - Circle Sectors with Trigonometry (Higher Only) - • Circle Sectors with Tr...
Part 10 - 3D Trigonometry - • The 5 Hardest 3D Trigo...
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Casio Fx-991ex Scientific Calculator Fx 991 Ex - New + 552 Function - Classwiz - amzn.to/2sw2Moz
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[@jameschester7839]

Seriously.. why is it that when you explain it I get this straight away but I spent a lesson completely stressed not understanding a word? You are the GOAT my bro thank you so much, got the last few right straight away after watching the first few 🤩🤩🤩

[@TheGCSEMathsTutor]

James Chester Haha well that’s great news!! Keep up the great work and thank you 😁🙏🏼

[@flapperpvp]

Seriously this is great

[@INeedGooderGrades]

@@flapperpvp you sitting your gcse's in 2024 too hmm or is a still a bit too early for you right now prevailing at this time?

[@steverobins5165]

These grade 9 hard question videos are literally the best vids out there. Keep doing what youre doing. Definitely will recommend you

[@TheGCSEMathsTutor]

Steve robins Thank you so much for the kind words 😁🙏🏼 I’ve got another one uploading on surds right now!!

[@unidentified5390]

Why are they called grade 9 questions?

[@shahcamranahmed9056]

@@unidentified5390 because they are worth grade 9.

[@unidentified5390]

@@shahcamranahmed9056 so grade 9 means u get 9 marks

[@shahcamranahmed9056]

@@unidentified5390 not really. Basically grade 9 questions are the hardest type of questions and are usually worth 5 or 6 marks. Any question that is lower than a grade 9 question would be worth less marks and easier to do than a grade 9 question e.g a grade 8 question or grade 7 question etc.

[@taod01]

Ngl ur videos are my new Netflix. Just turn it on the tv sit back relax watch how to do complex questions

[@TheGCSEMathsTutor]

Haha this is amazing! What a brilliant comment 🤣👏🏼 thank you for the kind words!!

[@taod01]

@@TheGCSEMathsTutor bruh i ain’t a rude guy or anything but my maths teacher sucks so bad so nowadays I just get home go on ur channel and learn what I missed out so thanks a lot mate

[@taod01]

@@TheGCSEMathsTutor bruh i ain’t a rude guy or anything but my maths teacher sucks so bad so nowadays I just get home go on ur channel and learn what I missed out so thanks a lot mate

[@onlineexamshelp9157]

We personalise teaching on the premise that every human being is uniquely made/created. Every students has intelligence that is unique and different from other students. Similarly learning abilities and styles also vary from student to student. Keeping in view this theory one on one class with student can help student more in learning than a combined class.Moreover, it would be easy for a teacher to assess student by pointing out weakness and work on them to enhance learning and performing best in the exams etc. This can only be made possible if a teacher is certified pedagogist and he/she excelled in subject/course teaching content with enough teaching experience. We offer following course individual tutorial/classes online. Mathematics: Grade 1-12 (IGCSE/A,O levels), Canada, USA, UK based syllabus Physics Grade 1-12 (IGCSE A/O levels), Canada, USA, UK based syllabus. English grammar and composition. Biology upto grade 8. Contact: [phone].. Skype: join.skype.com/invite/guqjw35byDPE

[@INeedGooderGrades]

@@taod01 why did you comment the same thing twice anyways same I genuinely do that too without practicing it in paper but I pause it and see if I am able to do it sometimes...

[@user-tg1zf6ow4o]

You’ve actually saved my life I used find these 3d trig questions hard but u made it look so easy thanks so much u don’t understand how much your videos helped me

[@fatimayusuf6206]

you are the best maths teacher! Pure gem!

[@TheGCSEMathsTutor]

Thank you so much! Really appreciate it 😁🙏🏼

[@kasadoesstuff]

You’re saving my maths mocks sir!! Thank you!

[@yashaswar1973]

I can tell that you put a lot of effort to make these brilliant videos Sir. Thank you so much!

[@Reubenn]

Thank you so much, just got them all correct so I'm feeling confident about the exam on Monday

[@particleonazock2246]

3D trigonometry is now a sinch for me, this video presented the concepts excellently and lucidly.

[@hirovvs1]

thanks blud ur the greatest of all time whats good in the hood gangy

[@i4TheWinN]

Love these "Top Hardest Questions" videos, gets me excited, very well explained sir, these videos will help everyone in the future, you're changing lives sir. Thank you.

[@TheGCSEMathsTutor]

Sacred Fσгτнεшιπ Great to hear, I’m glad they are working out for you! Thank you so much for the kind words 😁🙏🏼

[@matpatwary]

Your explanation is very simple and easy to understand every step... thanks lot

[@TheGCSEMathsTutor]

MAT PATWARY Great to hear! Thank you 😁🙏🏼

[@ho9506]

Thank you so much ! I have my maths tomorrow and am hoping to get an A so thank you very much for this

[@khadija2625]

Literally the most useful thing on the internet rn 👏🏽👏🏽👏🏽

[@charleyday4901]

I’m well annoyed, I’m in year 9, I just had a maths gcse higher test. The 2nd question you went through was a question that showed up on my non calculator test earlier this week. I have never learnt about cos and tan so I don’t understand how they expected us to do it. In the paper I worked out the ratio bit and that’s all I could do. But thanks for going through it it helps a lot

[@alinaseer5832]

you are an amazing teacher, your explanation is clear and to the point, really appreciate it. can you do a function walkthrough and hard questions?

[@TheGCSEMathsTutor]

ali naseer Thank you 😁🙏🏼 I’ve done composite functions and Inverse functions here - kzbin.info/www/bejne/e5W0ipZ3qNpqraM you can find the rest of the series in the playlist! I’m planning on doing another functions video this week too covering 5 difficult questions! 🤞🏼

[@alinaseer5832]

@@TheGCSEMathsTutoryou are a savior!

[@TheGCSEMathsTutor]

ali naseer Thank you 😁🙏🏼

[@onlineexamshelp9157]

We personalise teaching on the premise that every human being is uniquely made/created. Every students has intelligence that is unique and different from other students. Similarly learning abilities and styles also vary from student to student. Keeping in view this theory one on one class with student can help student more in learning than a combined class.Moreover, it would be easy for a teacher to assess student by pointing out weakness and work on them to enhance learning and performing best in the exams etc. This can only be made possible if a teacher is certified pedagogist and he/she excelled in subject/course teaching content with enough teaching experience. We offer following course individual tutorial/classes online. Mathematics: Grade 1-12 (IGCSE/A,O levels), Canada, USA, UK based syllabus Physics Grade 1-12 (IGCSE A/O levels), Canada, USA, UK based syllabus. English grammar and composition. Biology upto grade 8. Contact: [phone]. Skype: join.skype.com/invite/guqjw35byDPE

[@crazymemes2832]

how aqa felt after using this question on exam :☺😃

[@riaasx]

Sir I cannot thank you enough. Thank you SO much for your amazing videos! Keep it up, I will definitely recommend you to everyone who is struggling in maths!

[@harry-ji2pq]

Thank you so much for spending your time to help us. We all appreciate it :)

[@christinemilton5998]

Thank you for this. Your explanations are really thorough.

[@Masowe.]

i think i have improved a lot as i watch your videos. with this topic it was hard for me to know where to begin and i end up getting negative numbers..... i am looking forward to sit exams in NOVEMBER(UK) edexcel exams ...thank you so much,i will be watching other videos

[@TheGCSEMathsTutor]

COSTIE TV That’s incredible to hear! A little persistence goes a long way keep up the great work!! 😁🙏🏼

[@Masowe.]

@@TheGCSEMathsTutor thank you... i have to make a 9 with your videos and i am looking forward to see more !

[@shuali5720]

what score fid u get? I'm too looking forward for my edexcel exams in jan😭

[@Masowe.]

@@shuali5720 155/240 which us 2 marks away from 8

[@SanSan-gu6bb]

thank you so much for creating such kind of videos. They are super helpful.😊

[@ArmanTheLegend]

I find it hard to know which angle to work out when it ask for between something and the plane such as in 33:47. Why is it DAC the angle you're trying to work out?

[@onlineexamshelp9157]

We personalise teaching on the premise that every human being is uniquely made/created. Every students has intelligence that is unique and different from other students. Similarly learning abilities and styles also vary from student to student. Keeping in view this theory one on one class with student can help student more in learning than a combined class.Moreover, it would be easy for a teacher to assess student by pointing out weakness and work on them to enhance learning and performing best in the exams etc. This can only be made possible if a teacher is certified pedagogist and he/she excelled in subject/course teaching content with enough teaching experience. We offer following course individual tutorial/classes online. Mathematics: Grade 1-12 (IGCSE/A,O levels), Canada, USA, UK based syllabus Physics Grade 1-12 (IGCSE A/O levels), Canada, USA, UK based syllabus. English grammar and composition. Biology upto grade 8. Contact: [phone]. Skype: join.skype.com/invite/guqjw35byDPE

[@alitoto5452]

bro the same happened to me. I just played the video until he told me it's the angle DAC than I stopped it and did it in by my own

[@GCSEALevelMaths]

World class teacher keep this up sir!! Well done on 150k subs!!

[@INeedGooderGrades]

I think you should be watching the a level content of the gcse maths tutor

[@alphasaffi9230]

Wow you see eh im bless to have you in my career thank you very sir may the lord richly blessed you for being kind and show us the hidden facts about this topics

[@alberito4632]

you r my saviour thank you so much

[@speshial9957]

For question 2 please explain how b^ is 9.434 c =11.18^ and a^ =12.806?

[@dekcap5124]

i was confused too but just type it it in on a calculator and it right

[@aidonhook6262]

Is the volume of a cylinder provided in our exams? or is it a formula we have to memorise? Also, great vid- keep it up!

[@TheGCSEMathsTutor]

Aidon Hook Volume of a cylinder is one you need to know, but it’s just the area of a circle multiplied by the height of the cylinder 😁🙏🏼

[@nameerkhan9979]

If for the triangular prism question I got a slightly different decimal as an answer and then for the square-based pyramid I did have it rounded up to 73.6 in the exam, would I still receive full marks? Thanks

[@BobBob-uv9fq]

On the question where u half ,I get the a square and b square to be 2•5 as they are half of the square(actual square size) I get a different answer

[@officialaa165]

this was great thank you

[@TheGCSEMathsTutor]

Glad it helped!

[@momtazkhanom4336]

Please can you explain the differences between all the level 1 2 and 3 packages?

[@mohammedbismillah9078]

To multiply or divide When do I multiply and when do I divide

[@bro-gostudy_7665]

thank you so so much!!

[@helloig5686]

Sir i need to meet in real life to give u a hug

[@TheGCSEMathsTutor]

Haha! I’m guessing that means that you are enjoying the channel! 😂🙏🏼🙏🏼

[@helloig5686]

@@TheGCSEMathsTutor you are right indeed

[@calcpost3641]

Sir could you please do a video on enlargement, but not the transformation, where you have to cube root to find a side within a ratio from the volume , i find those very difficult

[@Jjjjjjjjjjjjjjjnjnnjj]

It’s called similarities

[@Tom-si9ls]

Nice video mate very useful

[@TheGCSEMathsTutor]

No problem at all! Glad to hear the channel is helping!

[@junaedahmed6677]

This Y u are mvp

[@alphasaffi9230]

My mentor thank you very much

[@joedewhurst1]

Thanks Pal

[@chandrakanthsangewar9341]

In 11:13, the second question, shouldn't 10 be the hypotenuse? I'm not sure.

[@alemi3d]

No he is correct to do so How's Lois by the way?

[@SP-sq6rr]

At 11:20, isn't 10cm the hypotenuse, instead of labelling it as the shorter side?

[@luminarahman1006]

you know,I'm thinking the same!

[@ecallaw1480]

I had the same question

[@onlineexamshelp9157]

We personalise teaching on the premise that every human being is uniquely made/created. Every students has intelligence that is unique and different from other students. Similarly learning abilities and styles also vary from student to student. Keeping in view this theory one on one class with student can help student more in learning than a combined class.Moreover, it would be easy for a teacher to assess student by pointing out weakness and work on them to enhance learning and performing best in the exams etc. This can only be made possible if a teacher is certified pedagogist and he/she excelled in subject/course teaching content with enough teaching experience. We offer following course individual tutorial/classes online. Mathematics: Grade 1-12 (IGCSE/A,O levels), Canada, USA, UK based syllabus Physics Grade 1-12 (IGCSE A/O levels), Canada, USA, UK based syllabus. English grammar and composition. Biology upto grade 8. Contact: [phone]. Skype: join.skype.com/invite/guqjw35byDPE

[@QuaternionPhysics1]

The hypotenuse is the side that is opposite the right angle. With triangle ABC, BC is the side that is opposite the right angle, so that is the hypotenuse, not 10cm

[@nehan681]

can you please do a video on 3d trig and phythagoras.i find it really hard

[@lemonnn.111]

Hey, Im having trouble downloading the worksheet, everytime I click on the download button it just pans to the top of the page. Having worksheets for topics like these does come in handy because it takes a lot of time to draw out each question. I hope the problem can be fixed, thank youu :D

[@MAN59724]

At 23:44 , how do you know the bottom right angle (A) is a right angle?

[@joshuabull3699]

picture the shape from a birds eye view and you should be able to see that it's a right angle because the bottom face of the shape is a rectangle so the corner is a right angle (hope that makes sense)

[@gOdhazZ]

how it ADH a right angle triangle for question 1, it doesn’t look like that bottom right is 90 degrees on the diagram.

[@kieratsahota6835]

How many Mark's in an exam would this be?

[@TheGCSEMathsTutor]

Kierat Sahota It would vary, most of these are around 4-5 marks 😁

[@kieratsahota6835]

Ok thanks

[@alphasaffi9230]

My mentor i said i will follow you like Ruth and Naomi

[@Xh-xg2ll]

Can somebody explain why on 8:07 there’s the inverse of tan?

[@rosaalnds]

Because you’re finding the missing angle that’s why anytime you want to find a angle you do inverse

[@nikta3679]

you legend

[@shanashuaib8651]

thankyou🥺🥺🥺🥺

[@mynameisntfin]

What does it mean by angle edh , how do you know what side the angle is meant to be on?

[@TheGCSEMathsTutor]

Trace your finger from E to D to H and the lines you draw over create only one angle 😁🙏🏼

[@afreenmurshida4838]

At 3:48 how did you know it was a right angled triangle? (Triangle ADH)

[@TheGCSEMathsTutor]

Afreen Murshida As AD is perpendicular to the base given the shape is a cuboid 😁🙏🏼

[@onlineexamshelp9157]

We personalise teaching on the premise that every human being is uniquely made/created. Every students has intelligence that is unique and different from other students. Similarly learning abilities and styles also vary from student to student. Keeping in view this theory one on one class with student can help student more in learning than a combined class.Moreover, it would be easy for a teacher to assess student by pointing out weakness and work on them to enhance learning and performing best in the exams etc. This can only be made possible if a teacher is certified pedagogist and he/she excelled in subject/course teaching content with enough teaching experience. We offer following course individual tutorial/classes online. Mathematics: Grade 1-12 (IGCSE/A,O levels), Canada, USA, UK based syllabus Physics Grade 1-12 (IGCSE A/O levels), Canada, USA, UK based syllabus. English grammar and composition. Biology upto grade 8. Contact: [phone]. Skype: join.skype.com/invite/guqjw35byDPE

[@farah4106]

why isn’t on 11:09 , that 10 is the hypotenuse?

[@hartds6393]

Woooow thank you so much!!

[@TheGCSEMathsTutor]

No problem 😊

[@mima4287]

You have used long way to find the angle...you should just subtract 64 from 90. Opposite angles are equal 26.

[@junnysun6200]

s-sir im so sorry but why do i got math error on my calculator when i put the cos inverse (ANS).... pls help thanks in adcvance!

[@sophiag3387]

For the 2nd question, I did the method correctly but I got answer wrong because when I was working out the individual lengths of each triangle I didn’t round them up & I kept them as their long whole answer. for the final calculation I got a different answer, but I thought in maths you’re not supposed to round up your working out until the very ended?

[@Thalasius]

I am so confused by this as well. Literally have the same issue.

[@cruzion4534]

Same i was stuck for a while on that

[@ambardhindsa4110]

thanks you sir

[@INeedGooderGrades]

what I thought 3D Trigonometry/pythagoras in terms of gcse questions can only be applied to certain shapes such as triangular prisms , cuboids and square based pyramids now ur telling me there's a cylinder involved?!?! wow examboard is crazy I'm not saying it was difficult its just that u gotta know the basic formulas for things like this.

[@jayhoa8249]

hello sir the worksheets are saying the website is updating

[@mirocairns-lowe3266]

may I ask in question two why do you use pythagoras and not soh cah toa?

[@erumfawwad1464]

Videos are brilliant as always,but the link for the worksheet never works :(

[@gabriellita7236]

Love the videos. But idk if it's just my phone or you should talk a bit louder

[@TheGCSEMathsTutor]

Thanks for pointing that out I’ll have to check across devices but it’s too loud on my phone I have to turn the volume down 😂 I just tested it from the top of a staircase and I could hear it! Have you tried headphones to see if that fixes the issue?

[@gabriellita7236]

@@TheGCSEMathsTutor thank you for replying so fast. I guess I will try buying some good headphone;as your videos are worth it.

[@_steph-xv7eb]

Why is there Pythagoras and sine and cosine in there it’s about trigonometry

[@aarontasawer5012]

Hey Sir i wanted to ask do You tutor students??

[@carrots3865]

for every trig question do you have to round it to 3dp? also thank you so much for this video! it's really helping me so much more than in lessons because you get right to the point and it allows me to focus more. thankyou!

[@blaiz7766]

it depends on you, but I recommend rounding to 2 decimal places so the answer will be more accurate

[@erumfawwad1464]

Pls guide how to downlaod the worksheets, it takes all information but the document is never emailed.

[@hime1552]

Hi, love your videos, this may seem like a really stupid question but why do we for example in the triangular prism question calculate the angle EMB instead of angle EMC. I guess I’m trying to say how do we know the base is B 😂

[@Jjjjjjjjjjjjjjjnjnnjj]

You take the easiest 90 angle you can see 😂😂 guess work but a good one

[@luminarymani]

25:43

[@RahimYeet]

just a question for the first one I got 25 degrees instead of 25.5

[@ainhis.m.k.6979]

33:51 why wouldn't they just ask to find angle DAC? it confuses me sm when they word it like that

[@drillman221]

yh they are some pricks lol. in real life , no one would word it like that but they gotta do what they can to make really hard questions I guess

[@alphasaffi9230]

Sir the diagram is not see clear please closer the video thank u sir

[@haseebplayz3993]

Hey sir, I've tried to download the worksheet but it isn't working and it isn't being emailed to me

[@TheGCSEMathsTutor]

If you go into the histograms worksheet you can download from there, currently fixing a glitch 🙏🏼

[@haseebplayz3993]

Thanks sir 🙏👍

[@tasneemkhalid284]

here 25:55 would it be correct if i found the third length and used the cosine rule instead or would i lose marks?

[@tacendamori]

if u got the right answer its fine

[@RobLevers-gj1dj]

What grade is the first question its the only one i can currently do

[@animeflix4359]

Grade 7

[@azzanwong557]

How you find 7.976 but not 8.0

[@rydhamkaur1898]

18:34 the answer is meant to be 81.5, you put the wrong thing in the calculator probably

[@bejewled]

uhh no he's right.

[@solyfede3275]

He is right you probably did a mistake somewhere

[@harisamaan786]

I got 4 right got the 4th one wrong I am trying to get a 8

[@TheGCSEMathsTutor]

Great work! 😁🙏🏼🙏🏼

[@harisamaan786]

@@TheGCSEMathsTutor can u do 3d pythagoras

[@alemi3d]

There is 99 comments and 999 likes on this video, Wtf?

[@TheGCSEMathsTutor]

Haha not for long! A rare find 😁🙏🏼

[@alemi3d]

@@TheGCSEMathsTutor man I thought this was sign from God

[@TheGCSEMathsTutor]

@@alemi3d Maybe it was… 🙏🏼

[@bejewled]

the ads are sooo irritating. i just wanna skip a bit then another ad then i need to skip more then another add

[@adithyan9263]

I'm in grade 12 and these looked a little hard to me , but in my defense i am an Indian does that count ? i don know 😁

[@vinaybhardwaj7811]

Hi, the UK GCSEs are the equivalent to Indian class 10th exams. :) But only one or two of these types of questions usually turn up in the exam, mainly for grade 9 students (toppers).

[@ieatalot4189]

44:49 the wording?? Rod??

[@alitoto5452]

I found it very difficult to know which angle to work out when it asks for. between something and the plane such as in 33:47. Why is it DAC the angle you're trying to work out?

[@bejewled]

because the question is asking for the angle between the line AD

[@rosaalnds]

@@bejewled yk for question 12 why do you draw it half way the line to TAC why did he only draw it to ta yk what I mean ?

[@mistermusab8055]

27:58