>> If the base of an equilateral triangle has a length of 1, what is >> its height?
Hint: Let's call this trangle ABC. Draw a line segment from A to the midpoint of BC (call it D). Note that line segment AD bisects angle A and is the height of the traingle. What can you now say about triangle ABD? With a little trig, you should now be able to solve for the length of AD.