Right Angle Triangles



From a given angle, we can name the sides of a right angle triangle:Adjacent is the side that touches the angle. Opposite is the side that does not touch the angle.*Note: The opposite and adjacent sides depend on the angle! If we look at the same triangle but a different angle, the opposite and adjacent sides will be different, but the Hypotenuse always stays the same! 428625016383000Identify the adjacent, opposite and hypotenuse sides for the angles in these right triangles:7810505842000 25050752476500Trigonometric Ratios The following triangles are similar.What do we know about the relationship between the sides of these triangles?In fact, any right angle triangle with these same angles will have the _______________ _________________! We give these ratios special names: SineCosineTangent These 3 are known as the ______________________ trig ratios. CosecantSecantCotangentThese 3 are known as the ________________________________________________ trig ratios.*These ratios Do Not Exist without the specified angle! Also, sin53.13° and sin22.62° refer to different sets of similar triangles.6762757620003019425-190500To remember the names of our primary trig ratios:Example 1 For the triangle below, finda) length of hypotenuse side b) length of adjacent side c) length of opposite side d) sinx e) cosx f) tanxExample 2 Calculate to 4 decimal places using your calculator. *A note on Calculators* Make sure that your calculator is in Degrees, not Radians, or all your numbers will be wrong! sin55° cos34°tan15° sin115° cos90° tan96° Using Trigonometric Ratios to Find SidesExample 31) First label the sides opposite, adjacent, hypotenuse.2) Then look at the side we have, and the side we want to find. 3) Check for which ratio has Adjacent and Hypotenuse. Example 4 Find the side x. Example 5 Using Trigonometric Ratios to find AnglesExample 1 Calculate the angle x to the nearest degree Now, we want x alone. To do this, we usually perform the opposite operation on x. For example when we have 2x=6, 2 is multiplying x, so we divide both sides by 2 to find x.The opposite operation for sin is sin-1. sinx=0.707cosx=0.259tanx=1.732sinx=0.848cosx=0.985tanx=-5.671Example 6 Finding angle a. Example 7Summary 1) Always label the triangles first: opposite, adjacent, and hypotenuse2) Figure out which ratio you need using 3) Solve for the unknown angle or side ................
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