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.
**
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 69º 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 37º 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 69º triangle has a horizontal leg x, and the 37º triangle has a horizontal leg ,x+36. The hypotenuse of the 69º triangle is the length of the guy wire, labeled L.
..
tan 69º=h/x
tan 37º=h/(x+36)
h=x tan 69º
h=(x+36) tan 37º
x tan 69º=(x+36) tan 37º
x/(x+36)=tan 37º/tan 69º=.2893
x=.29x+10.41
.71x=10.41
x=14.66 ft
..
x/L=cos 69º
L=x/cos 69º=14.66/cos 69º=40.9 ft
ans:
length of guy wire=41 ft
|
|
|
