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?
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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?