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February 7th copyright2009merrydavidson Happy Birthday to: Madison Bynum 1/27 Nick Arnold 1/30 Dana Barber 2/6 Krystal Carmona 2/6 Applications of Trigonometric Functions Section 4-8 Example 1: A bridge is to be constructed across a small river from post A to post B. A surveyor walks 100 feet due south of post A. She sights on both posts from this location and finds that the angle between the posts is 73. Find the distance across the river from post A to post B. x Post B Post A x tan 73 100 100 ft. 73○ It follows that x = 327. The distance across the river from post A to post B is 327 feet. Word problem means word answer! Bearings • We use bearings to describe the direction something is traveling or the direction in which we see something. A bearing measures the acute angle that a path or line of sight makes with a fixed north/south line. Reading Bearings • Many directions are given using a combination of two cardinal headings and degree number • North (N) and South (S) are always first • Then the number of degrees • Finally the East (E) or West (W) heading • Example: N 53° W Reading Bearings N 40º B A 20º W O 75º D C 25º S Bearing to A: N 70° E Bearing to B: N 40° W Bearing to C: S 15° W Bearing to D: S 25° E E Example 2 A boat leaves the entrance of a harbor and travels 40 miles on a bearing of S64E. How many miles south and east did the has the boat traveled? S64E 40 miles a cos 64 a b sin 64 40 40 cos 64 a b 17.5 a 40 40 sin 64 b 36 b 17.5 miles south, 36 miles east Alternate Bearing Method • Problems may just give you a single bearing • 130 degrees • This is always referenced from North clockwise to the bearing (heading). N 130 3) Draw a right triangle with right angle at C, angle A = 34.2 degrees, side “b” = 19.4 mm. Solve the triangle (solve means find all of the other B sides and angles). C 34.2 19.4mm A B = 55.80, a = 13.2 mm, c = 23.5 mm 4) A safety regulation states that the maximum angle of elevation for a rescue ladder is 720. A fire department’s longest ladder is 110 ft. What is the maximum safe rescue height? 104.6 ft 5) At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 350, whereas the angle of elevation to the to of the smokestack is 530. Find the height “s” of the smokestack alone. 125.4 ft. 6) A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end. Find the angle of depression of the bottom of the pool. top of water: 20m 7.70 1.3m 4m angle of depression 7) Draw a diagram that represents each bearing. a) b) c) d) e) bearing of 320 bearing of 300 N 420 E S 310 E N 520 W Homework Section 4-8; pg 359-361 Questions 16,18,20,22,30,36,37 Draw pictures, show all work for credit!