Math CentralQuandaries & Queries


Question from Katie, a student:

To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x - 2y = -2. Was is necessary to find the intersection point?


I am assuming that this is not meant to imply that this should be done without tables/calculator/etc as an approximation problem.

You need to find the angle each line makes with the x axis, and add (one slopes down, one up) If the answer is over 90 degrees, you've found the obtuse angle (there is no really easy way to tell in advance, it's easier to add first) and you must subtract from 180.

The slope of the first line is -2/3 . Its arctangent is 0.369 radians; multiply this by 180/pi and get (coincidentally!) 33.69 degrees. If you don't have a calculator to hand use Google: arctan(2/3) in degrees gets you your answer.

Good Hunting!


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