1. UNIT 5: TRIGONOMETRY Final Exam Review

2. TOPICS TO INCLUDE  Pythagorean Theorem  Trigonometry  Find a Missing Side Length  Find a Missing Angle Measure  Angle of Elevation and Depression  Area of a Triangle (SAS)  Area of a Triangle (SSS)

3. PYTHAGOREAN THEOREM  The Pythagorean Theorem is used to find MISSING SIDE LENGTHS in RIGHT triangles.  The theorem: a 2 + b 2 = c 2  a and b are the LEGS  c must be the HYPOTENUSE

4. PYTHAGOREAN THEOREM

5.  Now you try:

6. PYTHAGOREAN THEOREM  You can also use the Pythagorean Theorem to determine if a triangle is a RIGHT triangle  If you perform the Pythagorean Theorem and the equation is EQUAL, then the triangle IS a right triangle  If you perform the Pythagorean Theorem and the equation is NOT EQUAL, then the triangle is NOT a right triangle

7. PYTHAGOREAN THEOREM  Example A = 4, B = 10, C = 12 a 2 + b 2 = c 2 4 2 + 10 2 = 12 2 16 + 100 = 144 116 = 144 NO, the triangle is not a right triangle

8. PYTHAGOREAN THEOREM  Now you try: A = 9, B = 40, C = 41

9. TRIGONOMETRY  Trigonometry is used in order to find missing SIDE LENGTHS and missing ANGLE MEASURES in a right triangle  There are 3 trigonometric ratios  SINE  COSINE  TANGENT  In order to correctly find the missing side or angle, you must use the CORRECT ratio

10. TRIGONOMETRY  SOHCAHTOA  Sine  OPPOSITE over HYPOTENUSE  Cosine  ADJACENT over HYPOTENUSE  Tangent  OPPOSITE over ADJACENT

11. TRIGONOMETRY  Example Which trig ratio would you use? You would use TANGENTYou would use SINE

12. FINDING A MISSING SIDE LENGTH  To find a missing side length:  Determine which RATIO to use (sine, cosine, or tangent)  Set up the problem using the given ANGLE measure  Put a 1 under the trig ratio  CROSS multiply  Make sure your calculator is in DEGREE MODE

13. FIND A MISSING SIDE LENGTH  Watch this video for an example on how to find a missing side length

14. FIND A MISSING SIDE LENGTH  Now try this:

15. FINDING A MISSING ANGLE MEASURE  To find a missing angle measure:  Determine which RATIO to use (sine, cosine, or tangent)  Set up the problem using the given ANGLE measure  Use the INVERSE trig button in your calculator  Make sure your calculator is in DEGREE MODE

16. FIND A MISSING ANGLE MEASURE  Watch this video for an example on how to find a missing angle measure

17. FINDING A MISSING ANGLE MEASURE  Now you try: 1. 2.

18. ANGLE OF ELEVATION AND DEPRESSION  Angles of Elevation and Depression are used in WORD PROBLEMS in order to find missing angles and side lengths Angle of ElevationAngle of Depression  The Angle of Elevation and the Angle of Depression are ALWAYS EQUAL

19. ANGLE OF ELEVATION AND DEPRESSION  Now you try: 1.An escalator from the ground floor to the second floor of a department store is 110 ft long and rises 32 ft. vertically. What is the escalator’s angle of elevation? 2.From the top of a lighthouse 210 feet high, the angle of depression of a boat is 27 . Find the distance from the boat to the foot of the lighthouse. The lighthouse was built at sea level.

20. AREA OF A TRIANGLE (SAS)

21.  Try this one:  Find the area of the triangle

22. AREA OF A TRIANGLE (SSS)

23.  Now try this:  Find the area of the triangle

24. ALL DONE