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 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 A Side opposite A Side adjacent to A B C c b a S ine A ( Sin A ) = side O pposite A (a) H ypotenuse (c) C osine A ( Cos A ) = side A djacent A (b) H ypotenuse (c) T angent A ( Tan A ) = side O pposite A (a) side A djacent A (b))
Meet My Friend SOH CAH TOA S ine C osine T angent O pposite A djacent O pposite H ypotenuse H ypotenuse A djacent
Finding Trig Ratios D E F 14 48 50 Find Sin, Cos and Tan of D and E ** Round to nearest ten-thousandths Sin D = = 0.28 Cos D = = 0.96 Tan D = = 0.2917 Sin E = = 0.96 Cos E = = 0.28 Tan E = = 3.4286 Which ones are the same? Why?
Finding Trig Ratios 2 Check out Examples 1 and 2 on pages 558-559 Check out Examples 3 and 4 on pages 559-560 Does the size of the right triangle matter in Ex. 1? What is the determining factor for the trig ratio? What is true about the sin 45 o and cos 45 o ? Why is the tan 45 o = 1? If the sin 30 o = 0.5, then what is cos 60 o ?
Using Trig Ratios in Real-Life You can use trig ratios to calculate heights or distances. Find sin 36 o - you should have gotten 0.5878 Find tan 53 o - you should have gotten 1.3270 Put Calculator into DEGREE mode: Press MODE - make sure DEGREE, not RADIAN is highlighted FIRST - you need to be able to find the sin, cos or tan of an angle.
Using Trig Ratios in Real-Life What trig ratio uses opposite and adjacent? Tangent! tan 48 o = => 100(tan48 o )= h 100(1.1106) = approx 111 feet 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. Find the height of a building: 48 o 100 ft. h Pretend you’re standing at the angle.
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.