A rescue helicopter flew from its home base for 35 km on a course of 330 degrees to pick up an accident victim. It then flew 25 km on a course of 090 degrees to the hospital. What distance and on what course will the helicopter fly to directly return to its home base?

Question

anonymous · Answer

330 degrees is the same as 30 degrees to the southeast.

35cos(30 degrees) km east = 30.3108891324553 km east
35sin(30 degrees) km south = 17.5 km south

Next he flew 25 km due north

So overall, he flew 30.3108891324553 km east, and
(25 - 17.5) = 7.5 km north

So he must fly southwest to get back.

Fly south 7.5 km, and
Fly west 30.3108891324553 km

Magnitude of distance is sqrt(7.5^2 + 30.3108891324553 ^2) = 31.225 km (looks good so far)

Direction = 180 + arctan(7.5/30.3108891324553 ) = 194 degrees

anonymous · Answer

I'm looking at a unit circle and are you saying that 330 degrees southeast = 30 degrees northeast?

anonymous · Answer

how would it look like? like this:

|dw:1337881549579:dw|

anonymous · Answer

can someone please draw it out? I don't understand..

stormfire1 · Answer

Since this is a question involving navigation, you must use compass degrees...which is different than what a cartesian plane would show.

Here's a picture which should help...you just need to solve the triangle to find the length of the of last line (and angle) for the plane to get back to home base.