## The Problems

a) Phil packs his bags and takes a roadtrip up to Seattle. There he finds Seattle's Space Needle of

**605 feet**casting a

**410 foot**shadow at which Phil is standing at the end of. If Phil looks

**at the top**of the building (and avoids getting his eyes burnt by the sun) what is the

**angle**of Phil's eyes to the top of the building? (to the nearest hundredth of a degree AND assume Phil's eyes are

**5 feet above ground level**since he's a short little fellow.(http://upload.wikimedia.org/wikipedia/commons/3/38/BMX_aloft_and_Space_Needle_03.jpg)

**300 feet**

**where he can enjoy the panoramic view. But the mighty rock is slanted at its highest point, Phil estimates the angle of depression from where he is standing (at 300 feet) to the bone-crushing bottom to be**

**53***

**.**Should Phil fall, like the klutz he is, how long is his path to certain doom?

**(Round to the nearest foot.)**

http://triggerpit.com/wp-content/uploads/2012/01/sequoia-national-park-moro-rock.jpg

## The Solutions

a) Because it is from Phil's eye level of 5 feet we subtract 5 from 605 giving us 600. Its height is now 600 and the length is 410 which gives us the opposite (600) and adj (410) side. So we are looking for the angle (x). We use tan because of TOA and we use the inverse to undo tan to find our angle so it is tan -1 x (600/410) which is 55.65 degrees.

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