Question

I have two post that meet the ground perpendicular and the ground is level. One post is 40 feet high, the other is 25 feet high. If I draw a hypotenuse from the top of one post to the base of the other post and another hypotenuse from the top of the other post to the base of the first post, I need to find the height were the two hypotenuses intersect.

This is from Holt McDougal Larson Geometry 6.5 Exercises problem #38
If they meet at height h,

1/h = 1/25 + 1/40
h = 200/13 = 15.38

See wikipedia's article on the Crossed ladders problem for a discussion of the solution.

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