Answer
11.7
Work Step by Step
We call that altitude of the pentagon DM. Thus, we know that DM makes a right triangle with DB as the hypotenuse. However, we first find the height of DM:
$ DM = 8 + \sqrt{5^2 - 4^2 } = 8+3 = 11$
Thus, we use the Pythagorean theorem:
$ DB = \sqrt{11^2 + 4^2} = 11.7$
