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The TANgent ratio

The TANgent ratio. Leon Funchess. To start you off… . Okay, so when you have a right triangle, like so.

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The TANgent ratio

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  1. The TANgent ratio Leon Funchess

  2. To start you off… • Okay, so when you have a right triangle, like so • For angles A and B, the ratio of the opposite side to that angle to the adjacent side of that angle always stays the same, no matter what the measure of the angle. That ratio is the TANGENT RATIO.

  3. How to write it.. The writing above is how you would write the tangent ratio out, if you used the example to the right. You could also shorten it to be: The diagram above shows which sides to use to determine the tangent ratio.

  4. Examples!! Writing the ratio is very simple… you just have to follow the formula mentioned on the previous page, ------> but you have you sub in whatever the angle is for A. This one I’ll put up for you, but only because its your first time. Notice things like how the order flipped when you changed angles… but also note that the size of angle T or U doesn’t matter… it’ll still be opposite/adjacent.

  5. Here comes the calculations… By using the side lengths and/or the angles, you can find out various variables in a right triangle that is given to you in a problem. So let’s do this one together. Let’s start off by naming this angle X. to find W, you need to write out the equation first. tanX=opposite/adjacent. So to fill it in, you know that 10 is adjacent angle X, and w is opposite to it. And you also know that angle X = 54 degrees. So you fill everything in: tan54=w/10. then you simplify: 10tan54=w. then you put that into your calculator (SET IT TO RADIAN!!!!!!!!!!!!) and you should get about 13.76.

  6. PRACTICE For each one of the figures, figure out the value of W. Then Write out the tangent ratio for each of the triangles’ angles A and B. 1 B A B A 2

  7. Answers… Lolsike you can’t get them this early!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  8. The real answers…. Still not giving them to you!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  9. OKAY this is the real thing.. W=1.89 ratios: tanA=1/1.89 tanB=1.89/1 W=3.85 ratios: tanA=2.5/3.85 tanB=3.85/2.5

  10. The End • Okay, so that section was pretty easy and straightforward! I hope I helped you. If you need more help, look in section 8.3 of the textbook! Good luck on the finals everybody!

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