Answer
The height of the building is $ 10\sqrt{2}$ feet, or approximately $28.3$feet.
Work Step by Step
The situation describes resembles a right triangle where the hypotenuse is the 30-foot ladder and the base is the distance between the bottom of the ladder and the building, i.e. 10 feet. By re-arranging the Pythagorean Theorem $a^2 + b^2 = c^2$ to isolate the base of the triangle, we can solve for our missing variable in the following manner: $$a^2 = c^2 - b^2$$ $$a = \sqrt{c^2 - b^2}$$ $$a = \sqrt{(30)^2 - (10)^2}$$ $$a = \sqrt{900 - 100}$$ $$a = \sqrt{800}$$ $$a = \sqrt{2 \times 4 \times 10}$$ $$a = \sqrt{2} \times \sqrt{4} \times \sqrt{10}$$ $$a = 2\times 5\times\sqrt{2}$$ $$a = 10\sqrt{2}$$ $$a\approx 28.3$$
