Help Solving for x: 246.25 sin x - 676.58 cos x = -27768.42

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The discussion revolves around solving the equation 246.25 sin x - 676.58 cos x = -27768.42, with participants noting the limitations of sine and cosine values. It is highlighted that the equation may not be solvable as presented, and there is a suggestion that it could stem from an error in derivation. The main focus shifts to a related problem involving a pilot's navigation, requiring the use of Cartesian vector methods to determine the correct heading and travel time. A participant shares their work on the problem, but another points out a mistake in their calculations regarding the division by the plane's speed. The conversation emphasizes the need for accurate mathematical methods in solving vector-related problems.
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Hello, could anyone help me calculate the value of x?

246.25 sin x - 676.58 cos x = -27768.42

Thank you..

James
 
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You know the smallest value sin x can have, and the largest value cos x can have. So what is the smallest value 246.25 sin x - 676.58 cos x can have?


(Or are you expected to work with complex numbers?)
 
Ah, yea that's right. it's impossible to solve it.

Well, this equation is derived from somewhere else, and I might have done mistake in doing it.

This is the question:

Use Cartesian vector method to solve the problem. If you use any other method, you will receive zero.

A pilot wishes to fly form city A to city B, a distance of 720 km on a bearing of 70 degree. The speed of the plane is 700 km/h. An 60 km/h wind is blowing on a bearing of 110 degree. What heading should the pilot take to reach his or her destination? How long will the trip take?

Could you help me with this please? I will post my work in 5 minutes.
 
Last edited:
OK, here is my work:

http://i66.photobucket.com/albums/h242/jferdina/Bearing.jpg"
http://i66.photobucket.com/albums/h242/jferdina/Bearing-continued.jpg"
 
Last edited by a moderator:
As I see it, the last line is wrong, you divided the LSH by 700 but forgot to divide the RHS by 700. :)
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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