Dumb Question Dept. - Antenna Angle
 

I have a sloper that is 73 feet long.
The high end is 34 feet high, and the low end is 8 feet high.
What angle is the antenna?

It's a shame I can't figure out something I should have learned
in the 6th grade; but I don't know how to set the problem up.

Thanks,
Zack

Zachary Taylor wrote:

I have a sloper that is 73 feet long.
The high end is 34 feet high, and the low end is 8 feet high.
What angle is the antenna?

It's a shame I can't figure out something I should have learned
in the 6th grade; but I don't know how to set the problem up.

Thanks,
Zack

Easy answer. Do a web search for Trigonometry angle solver and you'll
discover that quite a few people have written little web sites where you
can enter in side-side-side lengths or side-angle-side and the remaining
angles and side lengths will be caluclated automatically.

I've used them. Don't feel bad, most of us have long forgotten
trigonometry.

Jimmy

"Zachary Taylor" wrote in message
...
I have a sloper that is 73 feet long.
The high end is 34 feet high, and the low end is 8 feet high.
What angle is the antenna?

It's a shame I can't figure out something I should have learned
in the 6th grade; but I don't know how to set the problem up.

Thanks,
Zack

Rise = 34-8 feet = 26 feet
hypotenuse = 73 feet

angle = arcsin of rise/hypotenuse = arcsin (28/73) = approximately 20.9°
between the ground and the wire.

The angle between a vertical support at the apex and the wire is then
90°-20.9° or 69.1°

"Zachary Taylor" wrote in message
...
I have a sloper that is 73 feet long.
The high end is 34 feet high, and the low end is 8 feet high.
What angle is the antenna?

It's a shame I can't figure out something I should have learned
in the 6th grade; but I don't know how to set the problem up.

Thanks,
Zack

arcsin(26/73)=20.86482
degrees

73, H.

Make a right triangle, with the sloper as the hypotenuse. One apex of
the triangle is the higher sloper wire end. Go straight downward from
there 34 - 8 = 26 feet to form the second side of the triangle. Then go
from there straight horizontally to the lower sloper wire end to form
the third side. The following isn't to scale, but it should give you the
idea. View it with your browser set to a fixed, not porportional, font:

/
/ |
sloper / |
73' / | 26'
/ |
/ |
/__A_______________|

The answer to your question requires basic trigonometry, usually taught
in high school in the U.S., so 6th grade math won't quite cut it. Of
course, you could draw it to scale on a piece of paper and use a
protractor to determine the angle, and that would be adequately accurate
for most purposes.

Angle A is the angle the sloper is tilted upward or downward from
horizontal. The sine of an angle in a right triangle = the length of the
side opposite the angle divided by the length of the hypotenuse, which
for angle A is 26/73. So we know that the sine of A = 26/73 = 0.356. In
this day and age, the way to find the angle once we know its sine is to
use a (scientific) pocket calculator. The function we want is "arcsin",
"ASIN", "inverse sine", or "SIN^-1", all of which mean "the angle whose
sine has this value". I notice that the calculator which comes with my
XP operating system (in the Accessories folder) has this function. If
you have one in your operating system, first make sure the "Degrees"
selection is made in the upper right (assuming you want the answer in
degrees). Then enter .356 into the calculator, check the Inv box (so
you'll get the inverse sine), and finally click the "sin" button. The
answer, with a ridiculous number of digits, is about 21 degrees.

You don't have to take a course in trig to learn and use the basic
functions sine, cosine, and tangent, which are just ratios of the
various sides of right triangles. (The cosine is the length of the
adjacent side divided by the length of the hypotenuse, and the tangent
is the length of the opposite side divided by the length of the adjacent
side.) With that knowledge and an inexpensive (or free) calculator, you
can easily solve problems like this.

Roy Lewallen

Zachary Taylor wrote:
I have a sloper that is 73 feet long.
The high end is 34 feet high, and the low end is 8 feet high.
What angle is the antenna?

It's a shame I can't figure out something I should have learned
in the 6th grade; but I don't know how to set the problem up.

Thanks,
Zack

On Sat, 27 Nov 2004 21:34:41 GMT, Zachary Taylor
wrote:

I have a sloper that is 73 feet long.
The high end is 34 feet high, and the low end is 8 feet high.
What angle is the antenna?

It's a shame I can't figure out something I should have learned
in the 6th grade; but I don't know how to set the problem up.

Thanks,
Zack

Hi Zack,

Well, not 6th grade material, but for my students in the Navy (and I
sure didn't invent this memory aid):

For the conventional usage
S sine C cosine T tangent O opposite A adjacent H hypotenuse
where you choose one corner or angle (but not the right angle) of any
right triangle and the terms mean:
O the length of the side Opposite that angle
A the length of the side Adjacent to the angle
H the length of the Hypotenuse

O
S = ----
H

A
C = ----
H

O
T = ----
A

What kept it in memory. Reading down columns gives
S C T O H A H O A
or
Sally Could Tell Oscar/Had A/Hard On/Always

You know the Opposite (26) and the Hypotenuse (73) which would give
you the sine (0.3562), take the arcsin of this value to find the angle
(21°).

73's
Richard Clark, KB7QHC

"Zachary Taylor" wrote in message
...
I have a sloper that is 73 feet long.
The high end is 34 feet high, and the low end is 8 feet high.
What angle is the antenna?

It's a shame I can't figure out something I should have learned
in the 6th grade; but I don't know how to set the problem up.

Thanks,
Zack



About 21 degrees. For calculation purposes, mentally move the antenna down 8
feet. So you now have a triangle with altitude of 26 feet and a hypotenuse
of 73 feet. The sine of the angle you want is 26/73 or .3562. The cosine of
..3562 is 20.86 degrees.

If you don't frequently use what you have learned, it evaporates. I know
exactly how you feel.

73,
John - KD5YI

On Sat, 27 Nov 2004 21:34:41 GMT, Zachary Taylor wrote:

[snip]

I'd like to thank everyone for the good (and quick!) answers.

This is a great group.

P.S. I just looked up someone I heard on the CW contest. Check out
his little antenna farm:
http://andor.net/ve6jy/ve6jy-siteinfo.html

And don't miss his little 80 meter yagi; it only weighs 1,200 pounds,
and yes, it rotates:
http://andor.net/ve6jy/ve6jy-80m.html

I'm glad envy can't kill, or we'd all be dead men

Zack

Zachary Taylor wrote:
I have a sloper that is 73 feet long.
The high end is 34 feet high, and the low end is 8 feet high.
What angle is the antenna?

It's a shame I can't figure out something I should have learned
in the 6th grade; but I don't know how to set the problem up.

Thanks,
Zack



SOH CAH TOA

Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent

34-8=26

So the Opposite is 26
the Hypotenuse is 73
Sin(theta) = 26/73 = 0.35616438356164383561643835616438

So Theta = ArcSin(0.35616438356164383561643835616438) =
20.864823641018812055586761532415 degrees

Or somewhere close to 21 degrees, if you're into rounding.

HTH

de AI8W, Chris

John Smith wrote:

About 21 degrees. For calculation purposes, mentally move the antenna down 8
feet. So you now have a triangle with altitude of 26 feet and a hypotenuse
of 73 feet. The sine of the angle you want is 26/73 or .3562. The cosine of
.3562 is 20.86 degrees.

If you don't frequently use what you have learned, it evaporates. . .

True enough -- "cosine" above should be "arcsin". The arcsin of a number
is the inverse sine, or the angle whose sine is the number. Cosine is a
different trigonometric function, defined by a ratio of different sides
than the sine.

Roy Lewallen, W7EL