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Trigonometry http://www.youtube.com/watch? v=t2uPYYLH4Zo Trigonometric Ratios There exists a ratio of side lengths of a right triangle which is the same for all similar triangles. Ex. The ratio of short _ leg hypotenuse of a 20-70-90 triangle is the same for all 20-70-90 triangles. TRIGONOMETRY Greek word meaning “measurement of triangles” Three Basic Trig Ratios hypotenuse c A B a Side opposite A C b Side adjacent to A side Opposite A (a) Sine A (Sin A) = Hypotenuse (c) Cosine A (Cos A) = side Adjacent A (b) Hypotenuse (c) side Opposite A (a) Tangent A (Tan A) = side Adjacent A (b)) Meet My Friend SOH CAH TOA Sine Cosine Tangent Opposite Adjacent Opposite Hypotenuse Hypotenuse Adjacent Finding Trig Ratios E 14 F 50 48 Find Sin, Cos and Tan of D and E ** Round to nearest ten-thousandths D 14 SinD = 50 = 0.28 48 CosD = 50 = 0.96 14 TanD = 48 = 0.2917 48 SinE = 50= 0.96 14 CosE = 50 = 0.28 48 TanE = 14 = 3.4286 Which ones are the same? Why? Finding Trig Ratios 2 Check out Examples 1 and 2 on pages 558-559 Does the size of the right triangle matter in Ex. 1? What is the determining factor for the trig ratio? Check out Examples 3 and 4 on pages 559-560 What is true about the sin 45o and cos 45o? Why is the tan 45o = 1? If the sin 30o = 0.5, then what is cos 60o? Using Trig Ratios in Real-Life You can use trig ratios to calculate heights or distances. FIRST - you need to be able to find the sin, cos or tan of an angle. Put Calculator into DEGREE mode: Press MODE - make sure DEGREE, not RADIAN is highlighted Find sin 36o - you should have gotten 0.5878 Find tan 53o - you should have gotten 1.3270 Trigonometry Trigonometry Using Trig Ratios in Real-Life Find the height of a building: You stand 100 ft. from the base of the building, the angle of elevation = 48 from a point on the ground to the top of the building. Pretend you’re standing at the angle. h 48o 100 ft. What trig ratio uses opposite and adjacent? Tangent! tan 48o = h(opp) => 100(tan48o)= h 100(adj) 100(1.1106) = approx 111 feet Using Trig Ratios in Real-Life Check out Examples 6 and 7 on page 561. Angle of Elevation = Angle formed by your line of sight from the horizontal upward. Angle of Depression = Angle formed by your line of sight from the horizontal downward.