SOLUTION: Here is the problem its a story problem. A guy wire to a tower makes a 69 degree angle with the level ground. At a point 36ft farther from the tower then the wire but on the same s

Question 477570: Here is the problem its a story problem. A guy wire to a tower makes a 69 degree angle with the level ground. At a point 36ft farther from the tower then the wire but on the same side of the base as the wire, the angle of elevation to the top of the pole is 37 degrees. Find the wire length to the nearest foot.
I seem to be having a hard time setting it up and figuring out what functions it uses. Any help is greatly appreciated!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Here is the problem its a story problem. A guy wire to a tower makes a 69 degree angle with the level ground. At a point 36ft farther from the tower than the wire but on the same side of the base as the wire, the angle of elevation to the top of the pole is 37 degrees. Find the wire length to the nearest foot.
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Draw a right triangle with the tower as the vertical leg, labeled h. From the base draw the horizontal leg which the right end makes a 69� angle of elevation with the top of the tower. Label this leg x. Extend this leg further to the right another 36 ft, the end of which makes a 37� angle of elevation with the top of the tower. You now have two right triangles to work with. Both triangles share a common vertical leg h. The 69� triangle has a horizontal leg x, and the 37� triangle has a horizontal leg ,x+36. The hypotenuse of the 69� triangle is the length of the guy wire, labeled L.
..
tan 69�=h/x
tan 37�=h/(x+36)
h=x tan 69�
h=(x+36) tan 37�
x tan 69�=(x+36) tan 37�
x/(x+36)=tan 37�/tan 69�=.2893
x=.29x+10.41
.71x=10.41
x=14.66 ft
..
x/L=cos 69�
L=x/cos 69�=14.66/cos 69�=40.9 ft
ans:
length of guy wire=41 ft
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