SOLUTION: If I have a 20 foot pole and want to hand Xmas lights from the top to the bottom with an angle of 15 degrees, how long does the strand need to be? Looking for formula as well.

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Question 815647: If I have a 20 foot pole and want to hand Xmas lights from the top to the bottom with an angle of 15 degrees, how long does the strand need to be? Looking for formula as well.
Thanks in advance.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If I have a 20 foot pole and want to hand Xmas lights from the top to the bottom with an angle of 15 degrees, how long does the strand need to be?
Looking for formula as well.
:
Assume you mean 15 degree from the top of the pole
This forms a right triangle so we can use the Cosine of the angle to find this
Cosine = Side Adjacent/hypotenuse
Angle = 15 degrees
Side adjacent = 20' pole
Hypotenuse = length of the strand to the ground (h)
Cos(15) = 20%2Fh
.9695 = 20%2Fh
.9695h = 20
h = 20%2F.9695
h = 20.7 feet, about 20' 8.5 inches
:
Formula for angle at the top
h = = pole+ht%2FCos%28angle%29
:
For angle from the ground
h = pole+ht%2FSin%28angle%29
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Response to comment
:
The radius of the circle would be the side opposite the top angle (15 degrees)
We could use the tangent of 15 to find that (side opposite/side adjacent)
tan(15) = r%2F20
r = 20 * .268
r = 5.36 ft or about 5'4" the diameter would be 10 ft 8 inches