11. A step ladder has two sets of legs. One set of legs is 8 feet long, and the other set is 7 feet long. When the ladder is opened the angle between the two sets of legs is 30o. How far apart are the sets of legs at the bottom of the ladder when it is opened up? How tall is the ladder when the legs are fully spread apart?

We can use the Law of Cosines to find the base

Taking square roots, we get

To get the height, it would help if we could find the angle at either A or B. At this point we can use the Law of Sines.

So the angle at A is

This gives us the height