SOLUTION: A 100-foot vertical tower is to be erected on the side of a hill that makes a 6* angle with the horizontal. Find the length of each of the two guy wires that will be anchored 75 fe
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Question 191436: A 100-foot vertical tower is to be erected on the side of a hill that makes a 6* angle with the horizontal. Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A 100-foot vertical tower is to be erected on the side of a hill that makes
a 6* angle with the horizontal.
Find the length of each of the two guy wires that will be anchored 75 feet
uphill and downhill from the base of the tower.
:
Treat this as two different triangles;
The uphill triangle: A= 90-6 = 84 degrees
Use the law of cosines: a^2 = b^2 + c^2 - 2(a*b)cos(A)
A = 84 degrees
a = guy wire length
b = 75'
c = 100'
:
a^2 = 75^2 + 100^2 - 2(75*100)cos(84)
a^2 = 5625 + 10000 - 2(7500)*.104528
a^2 = 15625 - 1567.9
a =
a = 118.56' length of the up-hill guy wire
:
:
The down-hill triangle A = 90+6 = 96 degrees
A = 96 degrees
a = guy wire length
b = 75'
c = 100'
:
a^2 = 75^2 + 100^2 - 2(75*100)cos(96)
a^2 = 5625 + 10000 - 2(7500)*-.1045
a^2 = 15625 - (-1567.9)
a^2 = 15625 + 1567.9
a =
a = 131.12' length of the down-hill guy wire
;
I'll leave it up to you to check my math here.
