A plane is is flying 225 mph heading S25°W. The wind is blowing S80°E at 60 mph.
What is the bearing of the plane?
What is the smallest angle of the triangle?
What is the largest angle of the triangle?
What is the remaining angle of the triangle?
What is the ground speed of the plane?
See Related Questions: Thu,5-25-11,11:28 AM.
To find the bearing of the plane, we need to calculate the resultant direction, taking into account both the direction of the plane and the direction of the wind.
The bearing is measured clockwise from north. We can start by drawing a diagram to represent the given information.
First, draw a line to represent the direction of the plane traveling S25°W.
Next, draw a line to represent the direction of the wind blowing S80°E.
Now, we can find the resultant direction by adding the vectors for the plane and the wind. We can do this by constructing a triangle and finding the direction of the diagonal.
To find the smallest angle of the triangle, we can use the Law of Cosines. The smallest angle will be opposite the shortest side of the triangle. In this case, the shortest side will be the side representing the wind since its magnitude is smaller than the magnitude of the plane's velocity.
To find the largest angle of the triangle, we can again use the Law of Cosines. The largest angle will be opposite the largest side of the triangle, which in this case is the side representing the plane's velocity.
To find the remaining angle of the triangle (the angle not opposite the wind or the plane's velocity), we can subtract the sum of the smallest and largest angles from 180 degrees.
To find the ground speed of the plane, we can use the Pythagorean theorem. The ground speed is the magnitude of the resultant velocity vector, which is the hypotenuse of the triangle formed by the plane's velocity and the wind velocity.
By applying these calculations to the given information, we can find the answers to all the questions.