Trigonometry Pile Up!

The idea for this resource woke me up from my sleep at about 4am the other morning! I must have been dreaming about one of Vi Hart’s amazing ‘maths doodle’ videos, in particular the one about The Triangle Party. I’m a big fan of Vi Hart’s Blog and the engaging, fast paced videos she produces. I love the way she crams in so much maths in the videos but ‘sells’ it as just interesting doodling!

This resource is a challenging puzzle to consolidate learning on trigonometry. The idea is that pupils have to start with the information they have in the bottom triangle and work their way up through the stack, finding missing side lengths to allow them to calculate the length of the hypotenuse of the top triangle. The puzzle can be solved with trigonometry alone (finding missing sides and missing angles) or Pythagoras’ Theorem can be used at some points as well.

This puzzle can also be used to clearly demonstrate why you shouldn’t round numbers mid-way through a calculation. It might be quite nice to get one group to round their answers at each stage to compare with the others and demonstrate how the rounding error accumulates through the puzzle.

There are lots of extension opportunities for this puzzle such as: what is the area of the whole compound shape?, what is the perimeter of the compound shape?, what proportion of the page is occupied by the triangles? etc…


Click here to download the resource


If you’re looking for a direct solution, this one is offered by @aap03102 :

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54 Responses

  1. Danielle Lewis says:

    Lovely resource, but only practising use of cos and Pythagoras. If you labelled some different angles, or orientated the triangles differently, it could also test whether students can choose correctly between sin, cos, tan and Pythag.

  2. Erika says:

    Love the Trigonometry Pile up!!

  3. I think this would be a great homework task! I like your idea of spliting up the group and making them round to different levels of accuracy to see what the error would be in each case. This would promote good discussion when they arrive back to class.

    It should also promote the idea of using working out as a way to spot your own mistakes. Those students who get the answer wrong and provide solid working out should be able to figure out where they went wrong.

  4. Amy says:

    Is there answers?

  5. Will Gibbs says:

    Whats the answer?

  6. Matthew Chang says:

    What is the answer?

  7. Frances says:

    I make it 12.07cm …?

  8. Julia says:

    I also got 12.07 cm

  9. Steffie says:

    I love the trigonometry pile up. Its so fun, but I still can’t find the one with all the other trig formulae though!

  10. Steffie says:

    I love the trigonometry pile up. Its so fun, but I still can’t find the one with all the other trig formulae though!

  11. zarina says:

    i got 14.2 cm

  12. This should have congruent triangle formulas. That would improve it a lot. SAS, SSS, etc.

  13. jessica says:

    whats the answer to the trigonometry pile up assignment due tomorrow.

  14. lynn says:

    I got 11.9 does anyone know if this is correct?

  15. Yolo Swag says:

    Bet y’all won’t show the work.

  16. Elise says:

    Did the newer version ever get uploaded? Where can I find it?
    Thank you! This looks great!!

  17. pritvi says:

    can u plz tell me the answer for this
    because it is too hard for me
    so plz any1 give me the answer

  18. Cheyenne says:

    Can I have the working out of the triangles

  19. Tiffany says:

    I got 14.71467129… using the exact values in the calculator. My students tried this and got answers as low as 11 if they rounded out to three places. This is a great tool to use to discuss rounding errors.

  20. max hotchin says:

    I got the answer as 11.7cm and im a school pupil anyone know if this is close or not please.

  21. Jackie says:

    I got 11.9cm – rounded to 1d.p the whole way. The answers cannot be given any more accurately than 1d.p as that is what is given on the puzzle.

    • Aslal says:

      If you want to round, the rounding always comes at the end. If you don’t do this, you get rounding errors. Also, since the bottom one has only one significant digit, that means that your answer would actually be 10 cm, instead of 11.9 cm (which, if you’re going off of all of the lengths and angles besides the bottom one, is still not rounded well. Every length and angle has only two significant digits, so your answer would be 12 cm if you’re rounding like this).

  22. Jim says:

    Will you please send me a copy of the updated project? Thanks. My email is

  23. Emily says:

    Some people in my class got 12.07 i originally got 15.18 but then did it again and got 12.05 and thought oh well its close enough we find out the answer tommorow

  24. Mathgeek says:

    The answer to that is on a calculator my friends

  25. Sam says:

    Can you please send me a copy of the updated project? Thank you. My email is

  26. js says:

    Would you please send me the link to the puzzle that uses all the trig functions as well?
    Thank you!

  27. rebecca tumlin says:

    I am so confused I don’t know where to start or how to start

  28. Lorraine Botha says:

    My learners enjoyed Trigonometry Pile Up very much but we would love to have the correct answer. Please send the follow-up using the other ratios as well. We can’t wait! Thank you

  29. Toys r us says:

    Can I have all the answers to the angles pls

  30. Dr G says:

    Hi, I dont agree with the long bracket solution at the top it has a mistake in the middle that should be tan 42 and eventually you get 12.1 as a solution

  31. Charlotte says:

    if there is an updated one with other trig functions could you send me this? I love this and have used it twice. kids of all abilities love this.

  32. Meredith Holmgren says:

    I would also love a link to the new version. This is a great activity!

  33. Alyssa Yada says:

    Thanks for sharing! I’d love a link to the new version.

  34. Steve Chong says:

    I got 8.3 cm… totally different to everyone else’s… I feel like I did it wrong

  35. Hannah says:

    I got 12.57 does anyone know if it is correct

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