The next problem involves directions in the form which we de

The next problem involves directions in the form which we defined in this section. Remember of bearing, bearing is always measured from a north-south line. Round all answers to the nearest integer A boat leaves the harbor entrance and travels 28 miles in the direction N35EThe captain then turns the boat 90®and travels another 16 miles in the direction S55°E. At that time, how far is the boat from the harbor entranceand what is the bearing of the boat from the harbor entrance? Distance from the harbor: miles Bearing from the harbor: S o W Get Help: Written example

Solution

When the boat is travelling North it goes a distance 28*cos35 in the northern direction. Then it goes South and moves 16*cos55 in a southerly direction so, in total, it goes North by
28*cos35 - 16*cos55 = 13.76 miles
Both directions went East so the boat moved East a total of
28*sin35 + 16*sin55 = 29.2 miles
The distance it is from the starting point is then
sqrt (13.76^2 + 29.2^2) = 32.3 miles
The direction it makes with the East is arctan (13.76/29.2) = 25.23 degrees = 90 - 64.77

so its bearing is N64.77E