Aship 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?

From the information given, the expression for the distance of the ship from the origin will be given by cosine rule:
c^2=a^2+b^2-2ab Cos C
From the information given:
c=distance from the origin
a=x, b=y, C=180-25=155
hence
c^2=x^2+y^2-2*x*ycos155
thus
c^2=x^2+y^2-2xycos155
hence to get c we get the square root of the above.
c=sqrt(x^2+y^2-2xycos155)