Dear lurkers:
The answer given by MacDorcha (8.6 ft) was right, but only the good Lord knows how MacDorcha computed it. The simplest way is to look up the sine of a 60 degree angle. If you're not equipped for that, there's another way. The other angle is 30 degrees, and most can remember enough high school trig (sine of 30 degrees is 5) to know how far the base of that the ladder is from the wall -- an even 5 feet. So even without some handy trig tables (or a slide rule which has them built in), one could rely on the ol' Pythagorean theorem to bang out the height, as we already know two of the sides of the triangle.
Even $5 calculators have "SIN" buttons nowadays. But I'd give him the points: usually when a student pokes the "SIN" button, the answer he writes down is 0.8666666.