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Lesson 7 – Trigonometry: The Tangent Ra4o Trigonometry is the study and applica4on of right angle triangles. When labeling triangles, typically the capital le?ers represent the _____ while their lower case equivalents represent the opposite __________. This would be called triangle ABC or ΔABC. Recall that if an angle is less than 90° it is called ________. An angle more than 90° is called ________. In a right angle triangle there is a right angle and two acute angles. In trigonometry the sides of a triangle are named in rela4on to one of the acute angles. Other than the ___________, or longest side, there will always be an opposite and adjacent side rela4ve to an acute angle. For any acute angle in a right triangle, the tangent ra4o is a comparison of the length of the opposite side to the length of the adjacent side. For any acute angle A: length of opposite side tan A = length of adjacent side Note that the tan ra4o depends only on the ____________ of the angle, not on the size of the triangle. (demo) Ex 1: Find tan X and tan Z in ΔXYZ. tan X = _____ tan Z = _____ The tan ra4o can also be used to find the measure of an angle if the sides are known. Ex 2: Find the measure of angle K and N in ΔKMN. tan K = ___ tan N = _____ K = tan-‐1 ___ N = tan-‐1 ____ K = N = Using the tan ra4o to solve word problems. Ex 3: A 10 b ladder rests against the side of a house with its base 4 b from the wall. Find the angle that the ladder makes with the wall.
