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Objectives: 1. To solve right triangles 2. To solve problems using directional bearings • • • • • • • Assignment: P. 359: 1-10 S, 13 P. 359: 15-21 S P. 359-360: 22-28 S P. 360-361: 29-36 S P. 361: 37-40 S P. 363: 63 c & d HW Supplement: 1 You will be able to solve right triangles When confronting a triangular problem in trigonometry, we usually abide by the convention that all right triangles are called 𝐴𝐵𝐶, where ∠𝐶 is the right angle and 𝑐 is the hypotenuse. Side a Opposite A Side b B Side c C If the legs of a right triangle are 3 and 4, what is the measure of the angle opposite the smallest side? To solve a right triangle means to find all of its sides and angles. Using trigonometry, what must you know to solve a right triangle? Solve the right triangle. Round your answers to the nearest tenth. You will be able to solve problems using directional bearings Getting lost was pretty easy to do in the days before your phone told you exactly where you were and where you needed to go. Navigators in those ancient days got around by finding their bearings. An aeronautical bearing is the clockwise direction between two points A and B measured in degrees relative to a North-South line (meridian). Meridian Fancy way of writing 71° “North “ can refer to either magnetic north or true north Navigators always use 3 digits when measuring a bearing so that 35° is never confused with 350°. Navigators always use 3 digits when measuring a bearing so that 35° is never confused with 350°. To distinguish themselves from pilots, sailors insist on using a different type of bearing. A nautical bearing is an acute angle measured in degrees from North or South, towards either East or West. To distinguish themselves from pilots, sailors insist on using a different type of bearing. A nautical bearing is an acute angle measured in degrees from North or South, towards either East or West. Convert the following aeronautical bearings into nautical bearings. 1. 035 2. 140 3. 260 4. 301 Convert the following nautical bearings into aeronautical bearings. 1. N 15 E 2. N 15 W 3. S 15 E 4. S 15 W What is the bearing from B back to A? A sailboat leaves its pier at a bearing of 270 at 8 knots (nautical miles per hour). After 15 minutes, the boat changes course to a bearing of 344 at 10 knots. Find the sailboat’s bearing and distance from the pier after 12 minutes on this course. Armed with a compass and an odometer, you set off on a bike trail consisting of two legs. The first leg takes you 20 miles at a bearing of 050, while on the second leg, you ride 12 miles at a bearing of 125. What is the distance, as the crow flies, from the starting point to your destination? What is the bearing? Objectives: 1. To solve right triangles 2. To solve problems using directional bearings • • • • • • • Assignment: P. 359: 1-10 S, 13 P. 359: 15-21 S P. 359-360: 22-28 S P. 360-361: 29-36 S P. 361: 37-40 S P. 363: 63 c & d HW Supplement: 1