A ship sails first N 80 o E

A ship sails first N 80 o. E for 120 nautical miles and then S 20 o. W for 200 nautical miles. How far is the ship from it’s starting point, and in what direction. Section 7. 6, # 79 To view this file, right click on the file and choose “full screen”.

Section 7. 6, # 79 North s ile m 0 2 80 o E es u 1 mil Port e nc sta 200 Di v South t or p to d 20 o W This distance from the port is the magnitude of vector d.

Find the components of vector u. 80 o 10 o u 120 s mile u = <a, b> a = 120 cos 10 o a = 118. 2 b = 120 sin 10 o b = 20. 8 u = <a, b> = < 118. 2, 20. 8 >

Section 7. 6, # 79 North u = < 118. 2, 20. 8 > s ile m 0 2 80 o E es u 1 mil Port e nc sta 200 Di t or p to d v 20 o W South

Find the components of vector v. mil d = 200 sin 250 o d = -187. 9 20 o 200 c = 200 cos 250 o c = -68. 4 es 250 o v v = <c, d> = < -68. 4 , -187. 9 >

Section 7. 6, # 79 North u = < 118. 2, 20. 8 > v = < -68. 4 , -187. 9 > 80 o E d = < 49. 8, -167. 1 > es u 120 d=u+v s mile |d| = mil Port e nc sta 200 Di t or p to d v 20 o W |d| = 174. 3 miles or 174 miles South

Find the direction from the port. Answers will vary. d = < 49. 8, -167. 1 > Find the reference angle tan q = -73 o q = tan-1 287 o d Answers: q = 73. 4 o E 73 o. S or E 287 o. N

Answers will vary. North q = 73 o Reference angle Answers: -73 o 287 o d E 73 o S or E 287 o. N 270 – 73 = 197 N 197 o. W

Answers will vary. q = 73 o Reference angle Answers: -73 o E 73 o. S or E 287 o. N 270 – 73 = 197 N 197 o. W 287 o d South 90 – 73 = 17 S 17 o. E