00:01
So in this question, they say that a 160 -foot tower is anchored on a hill by two guywine.
00:09
The angle of elevation of the hill is 6 degrees.
00:14
They say that each guywire extends from the top of the tower to a ground anchor that is 60 feet from the base of the tower and in line with the tower.
00:26
I want to find the length of each guywire, and then i'm going to...
00:31
Round to the nearest foot.
00:34
So they tell me that the angle of elevation of the hill is six degrees.
00:41
In other words, the hill itself makes a six degree angle with the horizontal.
00:51
And they told me that the height of this tower is 160 feet.
00:57
So just redrawing this a little bit, i've got my horizontal and i've got my hill and i've got this six degree angle here i have this tower that is 160 feet tall and then i have these two guy wires and they told me that each of these distances is 60 feet my trick this time is going to be to end up using the law of signs how am i going to do that well, i'm going to drop a perpendicular down here to the horizontal.
01:40
Now, if i do, what do i know about the angles in the triangle at hand? well, i know, first of all, that i have an 84 degree angle here, which means i have a 96 degree angle here, and then i have an 84 degree angle here.
02:07
So this is actually going to be a law of cosines question, since i have two sides and the included angle for each of these triangles.
02:19
So if i call these distances x and y, what can i say about x using my law of cosines? i can say that x squared is equal to 160 squared, plus 60 squared minus 2 times 160 times 60 times the cosine of 96 degrees.
02:47
So if i go to my calculator and i go into my degree mode, what am i getting here? well, again, i have 160 squared plus 60 squared minus 2 times 160.
03:10
Times 60 times the cosine of 96 degrees.
03:17
Now, of course, that's not x, that's x squared...