Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Applications and Models Objective: To solve a variety of problems using a right triangle. Example 1 • Solve the right triangle for all missing sides and angles. Example 1 • Solve the right triangle for all missing sides and angles. • The angles of the triangle need to add to 1800. 1800 – 900 – 34.20 = 55.80 Example 1 • Solve the right triangle for all missing sides and angles. a tan 34.2 19.4 0 19.4 tan 34.20 a 13.18 a 55.80 Example 1 • Solve the right triangle for all missing sides and angles. a tan 34.2 19.4 0 19.4 cos 34.2 c 0 19.4 tan 34.20 a 13.18 a 19.4 c cos 34.20 c 23.46 55.80 You Try • Solve the right triangle for all missing sides and angles. You Try • Solve the right triangle for all missing sides and angles. • The missing angle is 1800 900 280 620 You Try • Solve the right triangle for all missing sides and angles. 40 tan 28 b 0 40 b tan 280 b 75.23 62 0 You Try • Solve the right triangle for all missing sides and angles. 40 tan 28 b 0 40 b tan 280 b 75.23 40 sin 28 c 0 40 c sin 280 c 85.20 62 0 Example 2 • A safety regulation states that the maximum angle of elevation for a rescue ladder is 720. A fire department’s longest ladder is 110 feet. What is the maximum safe rescue height? Example 2 • A safety regulation states that the maximum angle of elevation for a rescue ladder is 720. A fire department’s longest ladder is 110 feet. What is the maximum safe rescue height? • We need to solve for a. a 0 sin 72 110 110 sin 720 a 104.6 a Example 3 • 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 top is 530. Find the height s of the smokestack alone. Example 3 • 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 top is 530. Find the height s of the smokestack alone. • First, we find the height to the top of the smokestack. as tan 53 200 0 200 tan 530 a s 265.41 a s Example 3 • 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 top is 530. Find the height s of the smokestack alone. • Next, we find the height of the building. a tan 35 200 0 200 tan 350 a 140.04 a Example 3 • 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 top is 530. Find the height s of the smokestack alone. • We subtract the two values to find the height of the smokestack. 265.41140.04 125.37 Example 4 • 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, as shown. Find the angle of depression of the bottom of the pool. Example 4 • 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, as shown. Find the angle of depression of the bottom of the pool. 2 .7 tan 20 2.7 tan 20 1 7.69 Trig and Bearings • In surveying and navigation, directions are generally given in terms of bearings. A bearing measures the acute angle that a path or line of sight makes with a fixed north-south line. Look at the following examples. Trig and Bearings • In surveying and navigation, directions are generally given in terms of bearings. A bearing measures the acute angle that a path or line of sight makes with a fixed north-south line. Look at the following examples. Trig and Bearings • You try. Draw a bearing of: W200N E300S Trig and Bearings • You try. Draw a bearing of: W200N E300S 20 0 300 Class work • Pages 521-522 • 2-8 even Homework • • • • Pages 521-522 1-7 odd 15-21 odd 27, 29, 31