4. 8.5 The Tangent Ratio

5.  Trigonometry  Greek word for “triangle measurement”  We will work only with right triangle trigonometry  Tangent is a ratio of the lengths of the legs of a right triangle.  Formula: A Adjacent leg Opposite leg

6. A B C 5 9 13 The mathematical abbreviation for tangent is tan. Whatever my angle I am dealing with then follows immediately afterwards. Finding the tangent ratio of the given angles.

7.  The tangent (function/ratio) explains the relationship between an angle and the sides opposite and adjacent that angle.  We can use the tangent function to find missing side lengths and to find missing angle measurements.

8. The tangent of an angle, depends only on the angles measurement.  Most calculators will allow you find the tangent of any angle measurement. For example, if you have a TI-83/84 you can simply type in tan(45) and it will spit out its value. Do not worry right now what that value means. If you have one of these calculators you must make sure that your mode is in degrees. Check by pressing the MODE button and going down and highlighting DEGREE..  Other calculators like the small TI-30x you have to push the 45 then find the tan function and press it.  So depending on your calculator you need to understand its order of operations.  The calculators that you will be using for the OGT allow you to simply type in tan(45) just like the TI-83/84.

9. With your calculator find the following  tan 45  tan 34

10. Sometimes you will be given the following  tan __?__ =5/8  If you are given what the tangent should be, then you need to solve to find out what the angle measurement is. The function on your calculator is called the “inverse tangent”.  On a TI-84 we just press that button and then plug in 5/8

11.  Find the following angle measurements.  tan__?__= 2/3  tan__?__=15/22  tan __?__ = 1  tan __?__ =.466308 These 2 actually tell you what the leg lengths are. The ones with decimals have already done the division and converted to ratio into a decimal.

12. Find the value of y to the nearest tenth. 15 ° y 21

13. Find z. 61 ° z 78

14. 23 ° y 9

16. Now we want to find an angle measurement given 2 known sides. We will use the tan -1 button Find this angle measurement 13

17. Now we want to find an angle measurement given 2 known sides. Find this angle measurement 13

18. Now we want to find an angle measurement given 2 known sides. Find this angle measurement 6 8

19.  A person at window W, 40 feet above street level, sights points on a building directly across the street. H is chosen so that WH is horizontal. T is directly above H, and B is directly below H. By measurement, m<TWH=61 and m<BWH = 37. How tall is the building across the street? 40 W H T B

20. Homework pg. 308 7-18, 21-24, 27  If looking for a leg, you will just use the tan button.  Remember to find an angle measurement you use tan -1