Math CentralQuandaries & Queries


Question from Inez, a student:

If you have a 30-60-90 triangle and the only side you get is 73 and a 90 degree box, how do you find the area?


I'm not sure exactly what you have but I think I can help. All 30-60-90 triangles are similar and I know the dimensions of one 30-60-90 triangle. The 30-60-90 triangle with hypotenuse of length 2 units has the other two sides of length 1 unit and √3 units, with the side of length 1 unit opposite the 30 degree angle. Thus if you have a 30-60-90 triangle with one side of length 73 units and you know which side it is you can use similar triangles to find the lengths of the other two sides.


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