Right AngleDate: 04/09/97 at 20:53:33 From: Raman Verma Subject: Right Angle I sure hope you can help me with this question. It goes like this: B C _____________________ |\ /| | \ / | | \ / | | \ / | | \ / | |_____\/______________| A P D The rectangle above has AB = 12cm and BC = 25cm. What value(s) for AP will make angle BPC a right angle? I pretty sure that you have to prove the two triangles similar (I think), but I don't know what to do after that. Date: 04/14/97 at 18:41:55 From: Doctor Wilkinson Subject: Re: Right Angle You've got the right idea; you just need to run with it. First of all, can you prove the triangles are similar? They're both right triangles, so you just need to show they have another pair of corresponding angles equal. All you have to go on is that BPC is a right angle. This suggests looking at the angles BPA and CPD, because these angles together with BPC make a straight angle. If you subtract out the right angle in the middle, you find that BPA and CPD add up to a right angle. From this you should be able to conclude that BPA and PCD are equal. Do you see how to do that? Now if you've got that far, then you know that triangles ABP and CPD are similar. What do you know about similar triangles? One thing you know is that they have corrsponding angles equal. But you already know that. What you want to use is the fact that corresponding sides are proportional. So let x be the length of AP. That makes the length of PD 25 - x, right? So one of the two similar triangles has sides 12 and x (we're not going to bother with the hypotenuses). The other one has sides 25 - x and 12. Clearly the 12 doesn't correspond to the 12, so it must be the other way around! So we have an equation which you should be able to solve: x/12 = 12/(25 -x) -Doctor Wilkinson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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