Wednesday, March 5, 2014

WPP #12: Unit O Concept 10: Solving angle of elevation and depression word problems

Our dear friend Phil has been struck with the wish to travel around the country, he's been bitten by the wander bug.

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.(

b) Once Phil gets tired of all the Space Needle this and Space Needle that, and the city overall in general, he heads over to Yosemite where Moro Rock lies standing tall at 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.)

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.

b) We know that the height is 300ft and the angle of depression to be 53*. We have the opposite side of 300 and we are looking for x which is the hypotenuse. Opposite and hypotenuse, SOH - Sin. So  this time it's sine of 53. So sin 53 = 300/x, we multiply by x on both sides which leads to us dividing 300 by sin 53 which equals approximately 758 feet. 

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