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7-2 Right Triangle Trigonometry

7-2 Right Triangle Trigonometry. Pull out those calculators!!!. Absolutes. Make sure the calculator is in degrees Scientific: Press DRG button till you see DEG on the face Graphing: Mode then toggle down and toggle left/right to degrees

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7-2 Right Triangle Trigonometry

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  1. 7-2 Right Triangle Trigonometry Pull out those calculators!!!

  2. Absolutes • Make sure the calculator is in degrees Scientific: Press DRG button till you see DEG on the face Graphing: Mode then toggle down and toggle left/right to degrees • Make sure you know how to find sin/cos/tan of angles Scientific: put in number, then press function Graphing: Function, number, enter

  3. Absolutes • If you have a sine or cosine value and want to find the angle, you will use sin-1 or cos-1. These are the inverse functions. Remember the definition of inverse: Put in the answer, get out the original (angle)

  4. Everything will be based on the triangle shown below. As it is called “Right Triangle Trig” you can assume there is a right angle. We will always have the right angle in the same place. B c a A C b Note: B = 42 means angle B = 42.

  5. Examples ΔABC is a right triangle with C = 90. Solve for the indicated part(s). • A = 42, b = 4; c = ? 2. b = 4, c = 7; B = ?

  6. Word Problems Before we do this, you need to understand 2 standard phrases: Angle of Elevation: ________________ ________________________________ Angle of Depression: _______________ _________________________________

  7. Examples • How tall is a tree whose shadow is 47 feet long when the angle of elevation is 49.3

  8. 4. One of the equal sides of an isosceles triangle is 23 cm and the vertex angle is 43. How long is the base?

  9. 8-1 Law of Cosines The first of 2 laws specifically for non-right triangles

  10. Notice: Non-right Triangles We will be using this law when the information given fits: • _________________________________ • _________________________________

  11. B c a A C b

  12. Area Formula B c a y x A C b

  13. Heron’s Formula • Used to find areas of triangles when all sides are given (SSS)

  14. Example Find the area of the triangle B 8 101 C A 12

  15. Example Heron’s • Given ΔABC with a = 3, b = 4 and c = 5, find the area using Heron’s Formula.

  16. Example 1. a=12; b=5; c=13 Find A

  17. 8-2 Law of Sines The second of 2 laws specifically for non-right triangles

  18. Again: Non-right Triangles We will be using this law when the information given fits AAS or ASA patterns.

  19. B c a A C b Law of Sines

  20. Examples • Solve ΔABC if a = 5, B= 75º and C = 41º. A=64º

  21. Example Tom and Steve are 950 ft apart on the same side of a lake. Rob is across the lake and he makes a 108 degree angle between Tom and Steve. Steve makes a 39 degree angle between Tom and Rob. How far is Tom from Rob?

  22. 8-2 Law of Sines

  23. Try this Solve ΔABC if a = 50, c = 65 and A = 57º What happened? a c A b

  24. a c c a A A b b c a c a A b A b

  25. a c c a A A b b c a c a A b A b

  26. How do we deal with this? When there are 2 triangles formed the B angles will be Supplementary. (Think Iso Triangle) C C b a a B B A

  27. What is the process to follow? If SSA triangle (given 1 angle) • _______________________ (csinA) • If only 1 ________________________ • If there are 2 triangles, ____________ • ________________________________________________________________. • ________________________________________________________________

  28. ExampleSolve for B and c: if A=53; a=12; and b=15

  29. Examples • If you solved it regular first and get “error” or “E” as a solution – that means that there is no triangle possible. **Good one to remember!!

  30. 2. Solve for ΔABC if c = 65, a = 60 and A = 57º

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