Question
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.
Answers
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
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