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01-27 Side Ratios for Similar Triangles

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    Now, I'm being a little cryptic here.
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    What do I mean by "ratios?"
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    Let's go back to our similar triangles to figure out what I mean.
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    Now, I have two triangles here.
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    They're similar because the angles match,
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    but the sides are different.
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    I'm going to label these sides a, b, c and these sides A, B, and C.
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    You can see that even though these sides are all longer,
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    there's some correspondence between A and side a.
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    Likewise with C and c and B and b.
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    But what exactly is that correspondence?
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    What do these things all have in common?
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    The fact is they have a ratio in common.
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    What I mean by that is they're linked through ratios.
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    If I look at the ratio side A to side B,
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    I'm going to find that's exactly the same as the ratio of side a to side b.
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    In fact, it doesn't matter how big or small I make this triangle,
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    this equality will always hold true.
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    And that's a really powerful mathematical tool that we can use.
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    For example, let's say I didn't give you variable names here,
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    but I gave you some actual numbers.
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    So, 3 m, 4 m and 5 m are replacing our sides from before,
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    and these are still unknown.
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    But let's say I told you that--I don't know--side B was equal to 6 m.
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    I can use this to calculate side C,
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    because I know that C/B has to equal, well, the corresponding sides--4/3.
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    More precisely 4 m over 3 m.
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    Notice that when we do this, the units cancel out,
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    so it doesn't even matter that we were using meters.
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    We could have been using inches or stadia or furlongs or any unit we'd like.
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    Now, I know this ratio--C/B--is equal to 4/3.
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    But notice that I have one other piece of information.
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    B is actually equal to 6 m, so let's write that in.
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    Now if I want to solve for C, I multiply both sides by 6 m,
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    and that gives me the following: C = 4/3 * 6 m, also known as 8 m.
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    Okay, that wasn't so bad.
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    We used the power of ratios to calculate an unknown side of a triangle,
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    and this is a huge tool to have at our disposal.
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    Can you do the same to solve for side A?
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    How long is side A in meters.
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    And you can just enter the number. You don't have to type in the m.
Title:
01-27 Side Ratios for Similar Triangles
Video Language:
English
Team:
Udacity
Project:
PH100 - Intro to Physics
Duration:
02:32
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