A ship sails x km due east to a point E and continues x km due north to F. Find the bearing the bearing of f from the starting point.

A ship sails x km due east to a point E and continues x km due north to F. Find the bearing the bearing of f from the starting point.

Answer Details

Let's draw a diagram to visualize the situation:

        N
        |
        F
        |
W-------+-------E
        |
        |
        S

The ship starts at the point marked "W", then sails east to reach the point marked "E". The distance between W and E is x km. Then the ship sails north from E to reach the point marked "F". The distance between E and F is also x km.

We want to find the bearing of F from W. This is the angle that the line segment WF makes with the north-south line, measured in a clockwise direction.

Let's call the point where the north-south line intersects the line WE as point G. Then we have a right triangle WGE, where WG is the distance travelled east by the ship, and GE is the distance travelled north. The angle WGE is the bearing we're looking for.

From the right triangle WGE, we can use trigonometry to find the angle WGE:

tan(WGE) = opposite / adjacent = GE / WG = x / x = 1

Taking the arctan of both sides, we get:

WGE = arctan(1) = 45 degrees

Therefore, the bearing of F from W is 045 degrees. Answer: (a) 045^o.