Math CentralQuandaries & Queries


Question from Oscar:

If I walked 620' and my compass was off by 8 degrees how many feet from my heading was I?
Thank You

Hi Oscar,

In my diagram (not to scale), $S$ is your start position, $P$ is the point where you planned to arrive and $Q$ is the point where you actually arrived. The angle $PSQ$ measures 8 degrees and $T$ is the midpoint of $PQ.$


The angles $PST$ and $TSQ$ are congruent (do you see why) and hence the measure of the angle $PST$ is 4 degrees. The angle $STP$ is a right angle (do you see why). What trig function relates $|TP|, |PS|$ and the measure of the angle $PST?$


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