pre cal
posted by Anonymous .
An antenna is on a hill that makes a 5 degree angle with the horizon. The antenna is placed so that it is perpendicular to the horizon. A guy wire extends from the top of the antenna to a point 50 ft downhill from the base of the antenna. If the antenna is 25 ft tall, what is the length of the guy wire.

pre cal 
Steve
As usual, draw a diagram.
Draw a horizontal line from the base of the wire to the base of the tower. (It will lie underground, but give you a right triangle to work with.)
If we label
T = top of tower
W = base of wire
B = base of tower
P = the point below the base of the tower where the horizontal line from B intersects.
Let u = BP
v = WP
u = 50sin5° = 4.36
v = 50cos5° = 49.81
wire length = √(v^2+(25+u)^2)
= √(49.81^2 + 29.36^2)
= 57.82
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