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
