# Airplanes

#### chopstixdcb

A plane travels 150 miles at a direction of 128°. It then changes direction and travels 185 miles at a bearing of 301°. How far is the plane from its original direction?

Please include steps and diagram if possible. Thanks.

#### spruancejr

Step 1: always draw a diagram in these situations.

Step 2: using your knowledge of trig, find x1, x2, y1, y2. (remember that x and y values can be negative depending on what quadrant they are in)

Step 3: add x1 + x2 and y1 + y2. Now you have your new values for how far the plane has traveled from its original position.

Step 4: using the origin as the initial takeoff point plot your new point using the x value and y value you found. The hypotenuse of the resulting new triangle will give you the distance.

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#### chopstixdcb

what was your distance from origin?

#### spruancejr

I'm not going to do your homework for you. I've given you all the steps necessary to complete and understand your problem. If you don't understand a specific part of the problem, I'll explain that part to you. The concept of this problem can be tricky to figure out but once you do the calculations are extremely simple.

mr fantastic

#### chopstixdcb

I'm asking so I can compare answers.

the distance i got from the original point was 329.5 miles...I just wanna make sure we got the same answers.

mr fantastic

#### spruancejr

That is an incorrect answer. Remember that the triangle in quadrant II has a negative x value and the triangle in quadrant IV has a negative y value. This will change your answer when you add them together.

#### chopstixdcb

That's weird, my teacher sent me the answer and she said I was correct. It might be my fault for posting the wrong question. I didn't mean from the original direction, I meant original point where the plane leaves. I'm still very lost with this though. I'm pretty sure that after drawing out the distance and directions, I should be left with one triangle and from there use Law of Sines or Law of Cosines...Help me please! Studying for my Pre-Calc Honors final T-T

#### spruancejr

You seem to be on the right track right now. Let me make sure that I am understanding your question correctly. A plane flies for 150mi at a bearing of 128 degrees. Then it turns to a bearing of 301 degrees relative to the initial 0 degree position and flies for 185mi.

#### chopstixdcb

I believe that after the 150mi it has traveled, we then take a 301 degree turn and travel 185mi. After it has traveled the 185mi, you find the distance from the take off point and ending point.

#### chopstixdcb

I'm very confused on how to draw this diagram.

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