A ship travels 250 km on a 230degree course. Find the distance it travels west and south, respectively.?

Question

I attempted the question... Is the answers 209.77 South and 40.32 West?

Please try to help me.

I want STEP BY STEP so I can learn the process not just the answer.....

I need an visual image of this....help

Answer 1

The ship's course makes an angle with the y-axis of 40 degrees
Since the hypotenuse is 250 we have
west distance = 250 sin 40 and south distance = 250 cos 40
sin40 = .6428 and cos 40 = .766
west distance = 250(..6428)=160.7 km
south distance = 250(.766)=191.5 km

Check 191.5^2+160.7^2 approximately = 250^2

Answer 2

I get 160.7 km west
191.5 km south

Your 230 degree course (picture this) is like the ship is headed toward the lower left corner of your screen, making a 50 degree angle with the horizontal. You have a right triangle whose hypotenuse is 250, the leg distance left/west is horizontal (250 cos 50);
the leg distance down/south is vertical (250 sin 50).

(I'm presupposing that you know in a right triangle that the adjacent leg of an angle divided by the hypotenuse = the cosine for that angle. The opposite leg from an angle divided by the hypotenuse = the sine for that angle.)

Modulo (below) makes a good point. I assumed that the 230 degrees was measured like any angle (from the + x-axis CCW; however, I have heard of navigation involving north as the orienting axis. If that is the correct perspective/interpretation in this case then the pertinent
50 degree angle is with the vertical (not the horizontal) and my original components need to be interchanged.

VISUALS (They're very hard to do on here!)

Answer 3

The ship travels along the hypothenuse, what they want is the other two sides.

Courses are plotted clockwise zero degrees at North.

Thus South is 180 deg, and this course is another 50 deg to the west from south.

So, sketch the triangle

So, you want the cos (230-180) is the South coordinate
and sin (230-180) is the West coord.

Like many math and physics problems, they are easy once you clearly understand the terminology. Btw, if you draw the line between two points using a Mercator projection, then that angle is your heading.