The idea for this task came about when a student looked at the 30, 60, 90 triangle and the given side lengths and realised that the triangle with missing length that I had drawn was similar to it. This meant that rather than substituting in an exact trig value and then solving the equation he just multiplied root 3 by 5 as the hypotenuse of the given triangle was 10 compared to the 2 on the 30, 60, 90 triangle I had initially showed them.
Anyway this is what I came up with to again encourage the idea of similar triangles being fundamental to why we can use trigonometry.
Follow this link to download an editable version: https://drive.google.com/file/d/1t-ihs4CYqcJjbWkcpB9IiEY5cnh2zcwF/view?usp=sharing
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