Need help solving

[delong]

A plane is flying from city A to city B, which is 120 miles due north. After flying 45 miles, the pilot must change course and fly N15oW to avoid a thunderstorm. If the pilot remains on this course for 25 miles, how far will the plane be from city B? Round your answer to the nearest mile.

Someone please help me solve this I cant figure out how to get the correct answer

-Thanks

 

[mmm4444bot]

… I cant figure out how to get the correct answer

Hello. What have you tried? Did you sketch and label the triangle? (A diagram is important.) The exercise provides one side length, you can determine another side length by subtraction, and you're given the measure of the angle between these two sides. You're asked to find the remaining side length.

When you have two sides and the angle between them, use the Law of Cosines to find the remaining side. Please show your efforts.

Also, take a few minutes to familiarize yourself with the forum's guidelines (aka: Read Before Posting announcement); you may start with this summary. Thank you! :cool:

(Your duplicate thread has been deleted.)

 

[Harmless Drudge]

A plane is flying from city A to city B, which is 120 miles due north. After flying 45 miles, the pilot must change course and fly N15oW to avoid a thunderstorm. If the pilot remains on this course for 25 miles, how far will the plane be from city B? Round your answer to the nearest mile.

Someone please help me solve this I cant figure out how to get the correct answer

-Thanks

One of two ways:

1: Break it into rectilinear pieces. That is to say, rectangles and right triangles. The first leg is a straight line segment, so take note of how far from the origin it takes you. Look now at the second leg, starting at the end of the first leg. It goes off at an angle. That angle, when combined with the horizontal and vertical lines emanating from the endpoints makes a right triangle. Those horizontal and vertical segments (the base and altitude of the resulting triangle) can be found with trig. Now you have the total displacement created by the second leg, as evidenced by the endpoint. Now you have your total displacement. If you are familiar with vectors, it is simple vector addition. If not, you just learned the basics.

2: Alternately, find the angle created by deviating from the vertical course. You know some side lengths, so the Law of Cosines demonstrates a ratio between all of the cosines and side lengths, regardless of the fact that it's not a right triangle.


So often in math, things hinge on viewing the same thing in two different ways. I would recommend using BOTH methods to familiarize yourself with how the pieces fit together. The first one, in particular, would be helpful if you are not yet familiar with vector addition.