1. Right Angle Trigonometry MoManufacturingWINs Precision Machining Technology ME 100 – Measurement, Materials & Safety

2. Remember that the three angles in a triangle add up to 180 degrees. If I know two of them the third one is simple to find. This angle Is the same as this angle Since these two lines are parallel These two angles must be equal The sum of these two angles is 180 degrees. They are said to be supplementary angles Some Basic Geometry you might need to be reminded about... These are called opposite interior angles

3. Basic right angle Trigonometry If: we have a triangle and one of the angles in that triangle is 90 degrees and we know the length of two sides or we know the length of one side and an angle We can compute all the dimensions of the triangle

4. Right angle Trigonometry is all about the ratios of the length of one side to the length of another. For a given angle that ratio remains the same regardless of the size of the triangle. Video on right angle trigonometry 7 minutes

5. Review/Learn Basic Right angle trigonometry concepts (Chapter 8 pg 168)

11. AngleSide Aa B 30b Cc.643 AngleSide Aa Bb Cc b a c c a b

12. c b a AngleSide Aa Bb Cc

14. TAN26Enter 2ndTan.4877Enter sin28° ‘ ‘’Enter9° ‘ ‘’ >Enter

15. Converting Degrees Minutes Seconds to Decimal Degrees and vice versa 20.45° to Degrees Minutes Note that in both cases we didn’t worry about the whole degrees. Only the portion to the right of the decimal or the minutes.

16. 28° ‘ “Enter5° ‘ ‘’>Enter° ‘ ‘’ Enter Should show 28.08333 28.5° ‘ ‘’Enter ° ‘ ‘’<Enter Should output 28°30´0´´ Convert Degrees Minutes Seconds into Decimal Degrees with calculator Let’s convert 28°5’ into Decimal Degrees Convert Decimal Degrees into Degrees Minutes Seconds Let’s convert 28.5 ° into Degrees Minutes Seconds

17. You should also take a look at the “law of Sines” and the “law of Cosines” These are used for determining the dimensions of “Oblique” triangles. In other words – triangles that are not right triangles. For any triangle ABC, as shown, the law of sines or sine rule states that We will first consider the situation when we are given 2 angles and one side of a triangle Example:

18. We will now consider the situation when we are given two sides and one angle of a triangle. In this particular example there are two possible triangles that could have a side of 10 units a side of 12 units and a non included angle of 56 degrees.

19. a, b and c are sides. C is the angle The Law of Cosines (also called the Cosine Rule) is very useful for solving triangles: It works for any triangle: The Law of Cosines When to Use The law of cosines is useful for finding: the third side of a triangle when you know two sides and the angle between them the angles of a triangle when you know all three sides

20. Other Resources.. Khan Academy You Tube videos STLCC Academic Support Khan Academy You Tube videos This workforce solution was funded by a grant awarded by the U.S. Department of Labor’s Employment and Training Administration. The solution was created by the grantee and does not necessarily reflect the official position of the U.S. Department of Labor. The Department of Labor makes no guarantees, warranties, or assurances of any kind, express or implied, with respect to such information, including any information on linked sites and including, but not limited to, accuracy of the information or its completeness, timeliness, usefulness, adequacy, continued availability, or ownership. This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.http://creativecommons.org/licenses/by/4.0/