Question

Locating Lost Hikers A group of hikers is lost in a national part. Two ranger stations receive an emergency SOS signal from the hikers. Station B is 75 miles due east of station A. The bearing from station A to the signal is S 60º E and the bearing from station B to the signal is S 750 W. 1. Draw a diagram that gives a visual representation of the problem. 2. Find the distance from each station to the SOS signal. 3. A rescue party is in the park 20 miles from station A at a bearing of S 80° E. Find the distance and the bearing the rescue party must travel to reach the lost hikers.

Answer 1

A 75 miles B 10° 20miles 600 27.45miles 750 53.03miles C

2 In A ABC, Here, LA: 30% 23= 15° LA + LB 30° +15" +Lc 180° +2C = 180° Lee 135° Now Ilse sine rule in A line din B b C sinA Sinc C Sin 30 sin 135° 75 a a= 75 x sin 30 sin 135" 75 / a = Voz BC = a = 53.03 miles

Sin B b Sin 15° Jiems sine c sine Sin 135 75 b ib 75 x fins 75° Sin 1350 AC= b = 27.45 miles Let the distance be d. ملا to reach lost hikers d = 1627.45)2 + 20% - 2 x(20)x(27,45) Los20 11.03 miles. . Becuring 27.45 sin 66° -20 sindo 27.45 cos 60° - 20 cos 80 S. 21.68°E