A boat traveling due north sees another boat traveling due east cross $800$ meters directly in front of it. The first boat is traveling at $4$ meters per second and the second is traveling at $3$ meters per second.

1. Find the angle (from due north) that a person on the first boat needs to angle his telescope to watch the second boat. Express your answer in terms of $t$, the number of seconds since the second boat was due north of the first.

   Hint 1(a):

   Draw and label a diagram.

   Diagram (a):

   

   Hint 2(a):

   Write an equation with $θ$ and $t$. Use sine, cosine, or tangent.

2. If the boat that is traveling north wants to catch the boat that is traveling east, what heading will the boat need to take and how long will it take to catch up to the eastbound boat?

   Hint 1(b):

   Draw a new diagram. The first boat will now travel on the diagonal.

   Diagram (b):

   

   Hint 2(b):

   Write equations with $θ$ and $t$. Use sine, cosine, tangent and/or the Pythagorean theorem.