91Ó°ÊÓ

A river has a constant current of \(3 \mathrm{~km} / \mathrm{h}\). At what angle to a boat dock should a motorboat capable of maintaining a constant speed of \(20 \mathrm{~km} / \mathrm{h}\) be headed in order to reach a point directly opposite the dock? If the river is \(\frac{1}{2}\) kilometer wide, how long will it take to cross?

A helicopter pilot needs to travel to a regional airport 25 miles away. She flies at an actual heading of \(\mathrm{N} 16.26^{\circ} \mathrm{E}\) with an airspeed of \(120 \mathrm{mph},\) and there is a wind blowing directly east at \(20 \mathrm{mph}\). (a) Determine the compass heading that the pilot needs to reach her destination. (b) How long will it take her to reach her destination? Round to the nearest minute.

At 10: 15 A.M., a radar station detects an aircraft at a point 80 miles away and 25 degrees north of due east. At 10: 25 A.M., the aircraft is 110 miles away and 5 degrees south of due east. (a) Using the radar station as the pole and due east as the polar axis, write the two locations of the aircraft in polar coordinates. (b) Write the two locations of the aircraft in rectangular coordinates. Round answers to two decimal places. (c) What is the speed of the aircraft in miles per hour? Round the answer to one decimal place.

Explain why the vertical-line test used to identify functions in rectangular coordinates does not work for equations expressed in polar coordinates.

Solve the triangle: \(A=65^{\circ}, B=37^{\circ}, c=10\).

Find the exact value of \(\sin \frac{7 \pi}{12}\).