two guy wires for a radio tower of SPI station made 60° and 58° as shown in the figure. if the ground anchors for each wire were 120 feet apart and assuming that the wires were straight, find the following
A. the length of each wire.
b. the height of the tower.
A. the length of each wire.
b. the height of the tower.
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Let:
x = distance at 60° angle
y = height of the tower
Solution:
@ 60° angle
tan60 = y/x
y = xtan60 -» Equation 1
@ 58° angle
y
tan58 = ------ -» Equation 2
120 + x
• Substitute Eq. 1 to Eq. 2
xtan60
tan58 = -------------
120 + x
tan58(120 + x) = xtan60
x = 1,457.98
• Height of the tower = xtan60
= 1,457.98(tan60)
Height of the tower = 2,525.30 ft
• Length of wire at 60°
cos60 = 1,457.98/x
x = 2,915.96 ft
• Length of wire at 58°
cos 58 = 1577.98/x
x = 2,977.77 ft