820 CHAPTER 8 Applications of Trigonometry Solve each problem. 1. Wires Supporting a Flagpole A flagpole stands vertically on a hillside that makes an angle of 20° with the horizontal. Two supporting wires are attached as shown in the figure. What are the lengths of the supporting wires? 2. Distance between a Pin and a Rod A slider crank mechanism is shown in the figure. Find the distance between the wrist pin W and the connecting rod center C. 3. Distance between Two Lighthouses Two lighthouses are located on a north-south line. From lighthouse A, the bearing of a ship 3742 m away is 129° 43′. From lighthouse B, the bearing of the ship is 39° 43′. Find the distance between the lighthouses. 4. Hot-Air Balloon A hot-air balloon is rising straight up at a speed of 15.0 ft per sec. A wind starts blowing horizontally at 5.00 ft per sec. Find the new speed of the balloon. What angle with the horizontal will the balloon’s path make? 5. Playing on a Swing Mary is playing with her daughter Brittany on a swing. Starting from rest, Mary pulls the swing through an angle of 40° and holds it briefly before releasing the swing. If Brittany weighs 50 lb, what horizontal force, to the nearest pound, must Mary apply while hold- ing the swing? 6. Height of an Airplane Two observation points A and B are 950 ft apart. From these points the angles of elevation of an airplane are 52° and 57°. See the figure. Find the height of the airplane. 7. Wind and Vectors A wind can be described by v = 6i + 8j, where vector j points north and represents a south wind of 1 mph. (a) What is the speed of the wind? (b) Find 3v and interpret the result. 8. Ground Speed and Bearing A plane with an airspeed of 355 mph is on a bearing of 62°. A wind is blowing from west to east at 28.5 mph. Find the ground speed and the actual bearing of the plane. 9. Property Survey A surveyor reported the following data about a piece of property: “The property is triangular in shape, with dimensions as shown in the figure.” Use the law of sines to see whether such a piece of property could exist. 10. Property Survey A triangular piece of property has the dimensions shown. It turns out that the surveyor did not consider every possible case. Use the law of sines to show why. Summary Exercises on Applications of Trigonometry and Vectors 30 ft 15 ft 15 ft 208 P C W Fixed pin Slider 25.58 11.2 cm 28.6 cm Track 408 B A 528 578 950 ft 21.9 yd 78.3 yd Can such a triangle exist? 388 509 21.2 yd 26.5 yd 288 109
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