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Section 4.3 Right Triangle Trigonometry Right Triangle Definitions of Trigonometric Functions Mnemonic device: SOH-CAH-TOA Trigonometry values for a given angle are always the same no matter how large the triangle is Example Find the value of each of the six trigonometric functions of if b=4 and c=2 5. c2 5 b4 Function Values for Some Special Angles Example Find the csc 300 , sec 300 , cot 300 Example Find the csc 600 , sec 600 , cot 600 Trigonometric Functions and Complements Example Find a cofunction with the same value as the given expression: cos 20o cot 40o Applications An angle formed by a horizontal line and the line of sight to an object that is above the horizontal line is called the angle of elevation. The angle formed by a horizontal line and the line of sight to an object that is below the horizontal line is called the angle of depression. Transits and sextants are instruments used to measure such angles. Example The irregular blue shape is a pond. The distance across the pond, a, is unknown. To find this distance, a surveyor took the measurements shown in the figure. What is the distance across the pond? 1200 yards The inverse function for tangent and the other angles can be accessed on your calculator the same way. Example A building is 40 feet high and it casts a shadow 36 feet long. Find the angle of elevation of the sun to the nearest degree. 40 feet 36 feet Find the cos . 1 3 3 10 10 (b) 3 10 (a) 10 10 1 (d) 10 (c) Find the height of the tree if the length of the shadow is 50 feet when the sun is at a 300 angle. (a) 25 feet (b) 25.56 feet (c) 28.87 feet (d) 30 feet 30o 50 feet