1. Lesson 9.10 Trigonometric Ratios Objective: After studying this section, you will be able to use trigonometric ratios to solve right triangles.

2. We can solve other triangles that are not specifically 30-60-90 and 45-45-90. We can use a table with the ratios already calculated. DegreesRadian MeasureSinCosTan DegreesRadian MeasureSinCosTan 00.00000 1.000000.00000 460.802850.719340.694661.03553 10.01745 0.999850.01746 470.820300.731350.682001.07237 20.034910.034900.999390.03492 480.837760.743140.669131.11061 30.052360.052340.998630.05241 490.855210.754710.656061.15037 40.069810.069760.997560.06993 500.872660.766040.642791.19175 50.087270.087160.996190.08749 510.890120.777150.629321.23490 60.104720.104530.994520.10510 520.907570.788010.615661.27994 70.122170.121870.992550.12278 530.925020.798640.601821.32704 80.139630.139170.990270.14054 540.942480.809020.587791.37638 90.157080.156430.987690.15838 550.959930.819150.573581.42815 100.174530.173650.984810.17633 560.977380.829040.559191.48256 110.191990.190810.981630.19438 570.994840.838670.544641.53986 120.209440.207910.978150.21256 581.012290.848050.529921.60033 130.226890.224950.974370.23087 591.029740.857170.515041.66428 140.244350.241920.970300.24933 601.047200.866030.500001.73205 150.261800.258820.965930.26795 611.064650.874620.484811.80405 160.279250.275640.961260.28675 621.082100.882950.469471.88073 170.296710.292370.956300.30573 631.099560.891010.453991.96261 180.314160.309020.951060.32492 641.117010.898790.438372.05030 190.331610.325570.945520.34433 651.134460.906310.422622.14451 200.349070.342020.939690.36397 661.151920.913550.406742.24604 210.366520.358370.933580.38386 671.169370.920500.390732.35585 220.383970.374610.927180.40403 681.186820.927180.374612.47509 230.401430.390730.920500.42447 691.204280.933580.358372.60509 240.418880.406740.913550.44523 701.221730.939690.342022.74748 250.436330.422620.906310.46631 711.239180.945520.325572.90421 260.453790.438370.898790.48773 721.256640.951060.309023.07768 270.471240.453990.891010.50953 731.274090.956300.292373.27085 280.488690.469470.882950.53171 741.291540.961260.275643.48741 290.506150.484810.874620.55431 751.309000.965930.258823.73205 300.523600.500000.866030.57735 761.326450.970300.241924.01078 310.541050.515040.857170.60086 771.343900.974370.224954.33148 320.558510.529920.848050.62487 781.361360.978150.207914.70463 330.575960.544640.838670.64941 791.378810.981630.190815.14455 340.593410.559190.829040.67451 801.396260.984810.173655.67128 350.610870.573580.819150.70021 811.413720.987690.156436.31375 360.628320.587790.809020.72654 821.431170.990270.139177.11537 370.645770.601820.798640.75355 831.448620.992550.121878.14435 380.663230.615660.788010.78129 841.466080.994520.104539.51436 390.680680.629320.777150.80978 851.483530.996190.0871611.43005 400.698130.642790.766040.83910 861.500980.997560.0697614.30067 410.715580.656060.754710.86929 871.518440.998630.0523419.08114 420.733040.669130.743140.90040 881.535890.999390.0349028.63625 430.750490.682000.731350.93252 891.553340.999850.0174557.28996 440.767940.694660.719340.96569 901.570801.000000.00000 450.785400.70711 1.00000

3. For some applications of trigonometry, you need to know the meaning of the angle of elevation and angle of depression. If an observer at a point P looks upward toward an object at A, the angle the line of sight PA makes with the horizontal PH is called the angle of elevation PH A Angle of elevation

4. If an observes at a point P looks downward toward an object at B, the angle the line of sight PB makes with the horizontal PH is called the angle of depression. PH B Angle of depression Note: Don’t forget that an angle of elevation or depression is an angle between a line of sight and the horizontal. DO NOT USE THE VERTICAL.

5. Example 1 Given right triangle DEF a. angle D to the nearest degree b. e to the nearest tenth FD E d = 11.2 e f = 20.1

6. Example 2 To an observer on a cliff 360 m above sea level, the angle of depression of a ship is 28. What is the horizontal distance between the ship and the observer? AC B 360 m x 28

7. Summary Summarize how you can use trigonometric ratios to solve everyday problems. Homework: Worksheet 9.10