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## A Bird's Eye View

Math brain teasers require computations to solve.

 Puzzle ID: #29492 Fun: (2.71) Difficulty: (2.58) Category: Math Submitted By: paul726

Jack sat in his father's office, atop a bookcase by the wide, floor-to-ceiling window. His father's employer had built this skyscraper right on the shoreline of the lake, directly across which stood the tallest tree in the state. Jack's view was spectacular, and, as he looked across the 866 ft. wide lake, he noticed something which he found interesting. When he gazed at the highest point on the tree, his line of sight was at a 30 degree incline above horizontal. When looking at the base of the tree, where it met the water at the far edge of the lake, he was looking at a 30 degree declination.

How tall is the tree?

Bonus: Later, after querying his father, he found out that the first floor of the office building was at ground level, and every subsequent floor was exactly 12 ft. above the one below. What floor is his father's office on?

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 paul726 Apr 02, 2006 I wanted to include a link for trig tables in the teaser, but forgot it. Here's one to use: http://www.math.com/tables/trig/tables.htm It's also been brought to my attention that the tallest tree on record was/is somewhere in the vicinity of 1/3 the height of this mythical tree. I guess if you can accept a 500+ ft. high office building build right at the edge of a lake, you can believe a tree being 1000 ft. high. monkey93 Apr 02, 2006 I guess I thought this was something to think about, but it was just a little hard...I'm not that good at proportions and math stuff, but I liked it. Vigo95 Apr 07, 2006 i'm done with you and you're tree !!!!! javaguru Feb 01, 2009 Pretty easy, but a nice teaser.