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A Bird's Eye View

Math brain teasers require computations to solve.


Puzzle ID:#29492
Fun:*** (2.72)
Difficulty:*** (2.6)
Submitted By:paul726Aus****!!




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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Draw a triangle from Jack's eyes, to both the base and the peak of the tree. Make a second triangle from the tree base to the bottom of the building, then up to Jack again.

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