Finding a Missing Side

Pre-Algebra · Axiom Academy

EXAMPLE Finding a Missing Side of a Right Triangle One ladder problem, both directions of a^2 + b^2 = c^2 : first find a missing leg, then find the hypotenuse. A window washer leans a ladder against a building. The wall, the ground, and the ladder always form a right triangle. Part 1 (find a leg): A 13-foot ladder is set with its base 5 feet from the wall. How high up the wall does the ladder reach? Part 2 (find the hypotenuse): Next, the washer must reach a window 8 feet up while keeping the base a safe 6 feet from the wall. How long a ladder is needed? Nice work — you used the Pythagorean theorem in both directions on one right triangle. Name the sides first: the hypotenuse is opposite the right angle and is the longest side; the other two are the legs. Find a leg: subtract before the square root — ft. Find the hypotenuse: add the squared legs, then square-root — ft. Whenever you know two sides of a right triangle, a^2 + b^2 = c^2 gives you the third.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.