<p>I'm probably overlooking some critical theorem or something because this is supposed to be a medium question, but I can't for the life of me figure it out. Here it is:</p>
<p>Image for the question:
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<p>In the figure above, line AE and line CD are each perpendicular to line CE. If x = y, the length of line AB is 4, and the length of line BD is 8, what is the length of line CE?</p>
<p>since x = y, they are both 45 degrees, and angle ABE = angle DBC, so both triangles in the picture are isosceles right triangles. so, sin <BAE = BE/AB means squareroot(2)/2 = BE/4, so BE = 2squareroot(2). Similarly, sin <CDB = CB/DB means squareroot(2)/2 = CB/8, so CB = 4squareroot(2). so CE = CB + BE = 6squareroot(2).</p>
<p>Thanks for the reply. That’s basically what I did but I still got it wrong.</p>
<p>…Because my calculator was set to Radians! D’oh!</p>
