Each side of an equilateral triangle measure 11 centimeters. to the nearest tenth of an centimeter, what is the length of the altitude

The length of the altitude is 9.5 cm.

The altitude bisects the base of the equilateral triangle (this is because the two sides emerging from the vertex are equal).  This gives us a right triangle with leg 5.5 and hypotenuse 11.  We use the Pythagorean theorem:

5.5² + h² = 11²
30.25 + h² = 121

Subtract 30.25 from both sides:
30.25 + h² - 30.25 = 121 - 30.25
h² = 90.75

Take the square root of both sides:
√h² = √90.75
h = 9.5