Similar Triangles and RatiosDate: 12/04/2002 at 20:43:20 From: Aida Subject: Math problem for a math test I tried but I just don't get it. My question is: A man who is 54.4 inches tall casts a shadow that is 69.7 inches. His son's shadow is 41 inches. What is the height of the man's son ? Date: 12/05/2002 at 12:02:26 From: Doctor Ian Subject: Re: Math problem for a math test Hi Aida, Here is a picture of the situation: | . 54.4 | . | . | . ? | . |_______ |_____ 69.7 41 The key principle here is that the triangles are 'similar' to each other, which means that even though they are different _sizes_, the ratio of any two sides in one triangle will be the same as the corresponding ratio in the other triangle. In this case, it means that 54.5 ? ---- = ---- 69.7 41 Two triangles are similar whenever all of their angles are identical. Imagine drawing a triangle on a sheet of paper, and then making a photocopy with the zoom set to something other than 100%. The lengths of the lines will change by the same amount - e.g., if one side is doubled, the other sides will be doubled as well - but the angles will remain unchanged. In other words, if you scale the size of a triangle, you end up with a triangle that is similar to the original triangle. And that's kind of what's happening here. The triangle for the man is a scaled ('zoomed') copy of the triangle for his son. Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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