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Where Is the Dot?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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Imagine the dot starts at the point $(1,0)$ and turns anticlockwise.

Estimate the height of the dot above the horizontal axis after it has turned through $45^\circ$.

Estimate the angle that the dot needs to turn in order to be exactly $0.5$ units above the horizontal axis.

Show how you can use Pythagoras' Theorem to calculate the height of the dot above the horizontal axis after it has turned through $45^\circ$.

Again, without resorting to Trigonometry, calculate the height of the dot above the horizontal axis after it has turned through $30^\circ$ and $60^\circ$?

Are there any other angles for which you can calculate the height of the dot above the horizontal axis?



The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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