(Standard 13) Suppose that high tide in Tacoma, Washington occurs at 9 AM and 9 PM, at which time the tide is 6 feet above the average sea-level. How long after 9 AM will the tide be back
down to only 3 feet above average?

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

(hint): the answer is in the question.