Wednesday, March 5, 2014

WPP #12: Unit O Concept 10: Elevation and Depression Word Problems


http://art-sci.blogspot.com/2012/02/statue-of-liberty-gone-wild.html

a). Sir Liftsalot just moved to Newark and is staring intently at the beautiful Lady Liberty from a distance of 19 feet. He looks up at a 71 degree angle in order to see the very top of that attractive statue. How tall is the statue? (not to scale)

b). Sir Liftsalot gets an awesome idea to take selfies from the top of the statue's head so that's exactly what he does. As he sends the selfies, he looks down from the statue at a friend who is 54 feet away from the statue on the ground. What's the angle of depression from Sir Liftalot's eye to his friend? (Assume that Sir Liftsalot's eye is 5 feet above the top of the statue and also be sure to get the height of the statue from the answer for part a).

Answers:

Part a).
1). First draw a picture of the problem. He is 19 feet away from the statue and he is looking up at 71 degrees. X represents the height of the statue, which we will be finding.
2). We have an angle, its adjacent, and its opposite so we will use tangent of 71 degrees = opposite/adjacent = x/19.
3). We want to solve for x so first thing we do is multiply by 19 on both sides.
4). We then get x is equal to 19 times the tangent of 71. Plug this into your calculator (make sure it's set to degrees!) and we get x = 55.18 (rounded) which means the statue is 55.18 feet tall.

Part b).
 

1). Draw the picture like so. Since we are using the height from Sir Liftsalot's eyes we will add on another 5ft to the height of the statue for an overall vertical length of 60.18. The horizontal value is 54ft since the friend is 54ft away. X represents the angle of depression, which we will be finding.
2). We know our opposite and our adjacent sides so we are going to use tangent to find the missing degree, x. We set this up as tangent of x = 60.18/54 as shown above.
3). Here is the remainder of the work. We will do the inverse of tangent on both sides to isolate x. We find that x is equal to 48.1 degrees (rounded). This means that the angle of depression was 48.1 degrees.



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