Question

A ship heads due north for x miles, then turns 25° east of north and travels for another y miles. which expression represents the distance the ship is from the original starting point?

Answer 1

The distance of the ship from the point of the origin can be determined through the trigonometric functions derived from the given distances and the angle. 

If we are to draw the ship with the distances traveled in the Cartesian plane, the abscissa (x-coordinate) and the ordinate (y-coordinate) can be determined as follow:

In the second part of the journey, the angle between the x-axis and the ship should be 90-25° = 65°

x-coordinate = y(cos 65°) = 0.4226y
2nd part of y-coordinate = y(sin 65°) = 0.906y

The first part of the y-coordinate is given to be x. 

Thus, the expression that can be used to determine the ship's distance from the original point is,

    d = sqrt ((0.4226y)² + (x+0.906y)²)

Answer 2

The first step to take is to draw a picture.  Acknowledging that the ship travels in a straight line (180 degrees), a turn of 25 degrees would result in 180-25 degrees, which is 155. Plug it into the equation:

z=√x²+y²-2(x)(y)·cosZ

√x²+y²-2(x)(y)·cos(155).