775 8.1 The Law of Sines Now use the form of the law of sines involving A, B, and b to find side a. a sin A = b sin B Law of sines a sin 31.10° = 347.6 sin 36.00° Substitute known values. a = 347.6 sin 31.10° sin 36.00° Multiply by sin 31.10°. a ≈305.5 ft Use a calculator. S Now Try Exercise 55. Solve for a. Recall that bearing is used in navigation to refer to direction of motion or direction of a distant object relative to current course. We consider two methods for expressing bearing. Method 1 When a single angle is given, such as 220°, this bearing is measured in a clockwise direction from north. Example: 220° 220° N Method 2 Start with a north-south line and use an acute angle to show direction, either east or west, from this line. Example: S 40° W 40° S A C E N N 428 158 b B 110 mi Figure 4 Solve for b. EXAMPLE 3 Applying the Law of Sines (ASA) Two ranger stations are on an east-west line 110 mi apart. A forest fire is located on a bearing of N 42° E from the western station at A and a bearing of N 15° E from the eastern station at B. To the nearest ten miles, how far is the fire from the western station? SOLUTION Figure 4 shows the two ranger stations at points A and B and the fire at point C. Angle BAC measures 90° - 42° = 48°, obtuse angle B measures 90° + 15° = 105°, and the third angle, C, measures 180° - 105° - 48° = 27°. We use the law of sines to find side b. b sin B = c sin C Law of sines b sin 105° = 110 sin 27° Substitute known values. b = 110 sin 105° sin 27° Multiply by sin 105°. b ≈230 mi S Now Try Exercise 57. Use a calculator and round to the nearest ten miles (two significant digits).
RkJQdWJsaXNoZXIy NjM5ODQ=