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