A boat going parallel to shore spots a lighthouse ahead on shore. The angle of the line from lighthouse to boat is 30 degrees. The boat sails 3mi, and now angle is 90. How far offshore is boat?
Consider the right angle triangle seen here: http://en.wikipedia.org/wiki/Right_triangle
Let, B: the location of the lighthouse, A: your past location (when the line formed an angle of 30 deg), C: your current location at 90 deg.
You know the angle at vertex A, ang(A) = 30 deg, and, b = 3mi, you are asked to determine small a. What is the relationship between ang(A), a, and b?
Here’s a diagram of the setting:
You want the distance $x$. It’s the length of one of the legs of a nice right triangle, and you know the length of the other leg. If you recognize this as a $30$-$60$-$90$ triangle and know the proportions of the sides in such a triangle $-$ and this is useful information that you probably should learn $-$ then you can get $x$ immediately. If not, you’ll need to use one of the trig functions of $30$°; do you know which one is useful here?