Math Help Needed

[LadyyRedd]

I'm helping my sister with some of her math homework, but it's been about 10 years since I've done this stuff. Can anyone help?

Here's the problem:

An airplane leaves an airport and travels for 100 miles in a direction of 300 degrees. How far north of the airport is the plane then? How far west?

Any help anyone can give would be appreciated.

Kimya

 

[Narnian_Princess]

Is this a graph problem? If so, is "North" at 0 degrees, and is 0 degrees on the top X axis or the right Y axis?

 

[mickman1962]

without just giving you the answer, think "triangle"

 

[LadyyRedd]

No, it's not a graph problem. I'm guessing it has to do with circles and arcs.

This isn't my homework, it's my sister's. Usually I know exactly how to do it and make sure she learns how to do it, I don't just give her the answer. But without knowing how to do it myself, I can't help her. I took all of this back in HS, but like I said, it's been 10+ years.

Kimya

 

[LadyyRedd]

without just giving you the answer, think "triangle"

Thanks, I'm still lost though.

Kimya

 

[LadyyRedd]

I got it. Someone PM'd me and gave me some very helpful hints. Thanks everyone.

Kimya

 

[damo]

Nevermind.

 

[RachelEllen]

This is a lot easier to draw than to explain! The only part I'm not completely clear on is what direction "300" degrees is. I am assuming it's northwest, because the question is asking you how far north and west the plane went. (Fair assumption?)

You need to create a right triangle and use some basic trigonometry.

Go to this Wikipedia page

http://en.wikipedia.org/wiki/Trigonometric_function

and scroll down to right triangle definitions. That way, we can talk about the same things. I'm going to substitude "east" for "west" because that's the way the diagram is.

First, draw your triangle: The plane starts from point A and travels up the hypotenuse. The length of "h" is 100 miles. Angle "A" is 60 degrees.


Now you just need to solve for the length of "a" to see how far north the plane is and "b" to see how east/west the plane is.

Sine A = a/h
Cosine A = b/h


You can look up the sine and cosine of 60 in a table and then just solve the equation.