Trouble Solving a Plane Flight Path Problem

[Mivz18]

I'm having trouble with this one problem:

A plane flies from base camp to lake A, 280 km away, in a direction of 20.0 degrees north of east. After dropping off supplies it flies to lake B, which is 190 km at 30.0 degrees west of north from lake A. Graphically determine the distance and direction from lake B to the base camp.

Well, I began by drawing the two paths making an angle of 30 facing west. Drawing the third path to make a triangle, I then find the vector x and y components. After I get all my numbers and finish calculating, I get an answer of close to 400 km and 50 degrees south of west. However, the book gives an answer of 310 km at 57 degrees south of west. Any guidance or suggestions as to what to do?

 

[HallsofIvy]

"Two paths making an angle of 30 facing west"? What does that mean?

Since the first leg is "north of east" and the second leg is "west of north" you certainly won't wind up SOUTH of west.
It is standard to take north "up" and east "to the right". If you do that then the first leg can be represented by a line of length 280 at 20 degrees above the horizontal . The second leg will be a line, starting at "lake A", of length 190, 30 degrees to the left of the vertical (and so 90-30= 60 degrees above the horizontal).

The first leg is (by "alternate interior angles") 20 degrees below that same horizontal.
The angle between the two legs is 60+ 20= 80 degrees.

Drawing the third leg to form a triangle gives you a triangle with two sides of length 280 and 190, with an 80 degree angle between them. You can use the "cosine law" to find the length of the third side and the sine law to determine the angles.

 

[wais]

There are a few things that could potentially be causing the discrepancy between your answer and the one provided by the book. First, it's important to double check your calculations to make sure there are no errors. Sometimes, a small mistake in one step can lead to a significantly different final answer. It may also be helpful to label your diagram and clearly define the angles and distances involved in the problem to ensure that you are using the correct values in your calculations.

Additionally, it's possible that the book is using a different method or approach to solve the problem. It may be worth looking at the solution provided and trying to understand the steps they took to arrive at their answer. This can help you identify any differences in approach or assumptions that may have led to the difference in results.

In any case, don't get discouraged if you're struggling with a problem. It's common to encounter difficulties while solving math problems, and it's important to keep trying and seeking help when needed. You may also want to discuss the problem with your teacher or classmates to see if they have any insights or tips that could help you reach the correct answer. Good luck!