Your South American expedition splits into two groups: one that stays at home base, and yours that goes off to set up a sensor that will monitor precipitation, temperature, and sunlight through the upcoming winter. The sensor must link up to a central communications system at base camp that simultaneously uploads the data from numerous sensors to a satellite. In order to set up and calibrate the sensor, you will have to communicate with base camp to give them specific location information. Unfortunately, the group’s communication and navigation equipment has dwindled to walkie-talkies and a compass due to a river-raft mishap, which means your group must not exceed the range of the walkie-talkies (3.0 miles). However, you do have a laser rangefinder to help you measure distances as you navigate with the compass. After a few hours of hiking, you find the perfect plateau on which to mount the sensor. You have carefully mapped your path from base camp around lakes and other obstacles: 550 m West (W), 275 m S, 750 m W, 900 m NE, 800 m W, and 400 m 30.0° W of S. The final leg is due south, 2.20 km up a constant slope and ending at a plateau that is 320 m above the level of base camp.

(a) How far are you from base camp? Will you be able to communicate with home base using the walkie talkies?

(b) What is the geographical direction from base camp to the sensor (expressed in the form θ° south of west, etc.)?

(c) What is the angle of inclination from base camp to the detector?