[chiekokiyoko]

As it passes over Grand Bahama Island, the eye of a hurricane ismoving in a direction of 18degrees north of west with a speed of 48km/h. Three hours later it shifts due north, and its speed slows to 87km/h.
How far fro Grand Bahama is the eye 4.5 h after it passes over the island? Answer in units of km

[Celine91]

you have to draw the geometry of this problem first, starting point of eye of hurricane is O with coordinates (0,0), moves 18 deg. north of west, this makes line A 18 deg. up of the negative x-axis side, or 72 deg. left of the positive y-axis.
Within 3 hours it moves 48 km/hr * 3 hrs = 144 km. At this point, hurricane shifts due to north, this makes another line B, parallel to y-axis in an upwards direction. For 1.5 hrs (4.5-3 hrs) within speed of 87 km/hr, so AB is 130.5 km.

what we have to do now is to connect line OA with line AB, so we get a triangle, the third unknown side (OB) length is the distance required to calculate. (again draw the geometry so you understand the problem), use law of cosines in triangle to calculate the third side (google search it if you don't know the law equation). OB = 222.2168 km (angle between OA and AB is 108 deg.)

==> Answer = 222.2168 km. (total distance traveled by hurricane from Grand Bahama Island in 4.5 hours)