February 7 th 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. It follows that x = 327. The distance across the river from post A to post B is 327 feet. Post B Post A 100 ft. x 73 ○ Example 1: Application 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

W N E S A B C D O 40º 75º 25º 20º Reading Bearings Bearing to A:N 70° E Bearing to B:N 40° W Bearing to C:S 15° W Bearing to D:S 25° 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 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 sides and angles). B = , a = 13.2 mm, c = 23.5 mm

4) A safety regulation states that the maximum angle of elevation for a rescue ladder is A fire department’s longest ladder is 110 ft. What is the maximum safe rescue height? ft

5) At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 35 0, whereas the angle of elevation to the to of the smokestack is Find the height “s” of the smokestack alone 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 Pool floor 1.3m 4m angle of depression 7.7 0

7) Draw a diagram that represents each bearing. a)bearing of 32 0 b)bearing of 30 0 c)N 42 0 E d)S 31 0 E e)N 52 0 W

Homework Section 4-8; pg Questions 16,18,20,22,30,36,37 Draw pictures, show all work for credit!