



 
Ken, Wonderful question! You have made some very important observations. Your question shows impressive insight; what you have done is to discover for yourself the idea behind trigonometry. Fortunately, others have done all the hard work, so that the answer to your question comes down to using a calculator (or computer, if you prefer). The relationship you seek is called the TANGENT of the angle. It turns out to be more convenient to use HALF the base of your isosceles triangle. Half of your isosceles triangle is a RIGHT TRIANGLE whose height h equals the height of your isosceles triangle, and whose base equals 5. The tangent of the base angle  call it x and measure it in degrees  is then h/5, so that \[h = 5\times \tan x.\] For example, Chris  


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