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.
