Word problem involving the pythagorean theorem
a 12-ft ladder leans against the side of a house. the bottom of the ladder is 6-ft from the side of the house. how high is the top of the ladder from the ground ? if necessary, round your answer to the nearest tenth.
? ft

You can look at this as a triangle. The 12 ft ladder is the hypotenuse (c). The 6 ft distance at the bottom is a leg (a), and the unknown height is also a leg (b). So we don’t know the height, it’s variable will be x. The pythagorean theorem is a^2 + b^2 = c^2. the formula will be x^2 + 6^2 = 12^2. Solve as worked out in the picture, your answer is 10.4.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584