I went there as well as quite a few other sites.
Unfortunately my watch has the standard log scales and the time scale with no room to fit in the sine scales described on this site.
I made the mistake of quickly loging in here before I went to bed last night and after reading Ben's sine thread and googling, over 2 hours later I still hadnt found what I was looking for. I did read a lot about slide rules - if only I could remember half of it <img src="/images/graemlins/smile.gif" alt="" />

I cant beleive they are charging those amounts and that people are buying them.

I never liked the Texas Instruments sci calcs, I went for the Sharp el-5 series because I found them easier to use.
Ive always got a Sieko Pilot watch on my wrist and mostly carry an iPaq in my pocket.
You get some funny looks when you start calculating with the watch, especially from the 10 to 15 year old age group.

Your pilot watch just has the C and D scales on it, no trig scales. That means that unless you've memorized the sines of some reference angles, you're stuck. That's a pity, because the slide rule would be a great, reliable, fast way to do that calculation. Chained multiplications and divisions, with no addition or subtraction, is where they shine.

There is a Japanese company which makes pocket-sized circular scientific slide rules which would be great for that use, and they're quite reasonably priced. Their number 270 (see here) would do the job, and it's only about $20. Unfortunately, they want 10,000 yen to ship to the U.S. That's about $100, so I haven't bought any of their $20 slide rules yet. Maybe some day I'll stop in Japan and find one in an airport gift shop.

> Essentially, all you need is two sides and one angle of the triangle, or one side and two angles.

Although you may need the cosine rule rather than the sine rule. The cosine rule is more complicated: it says: sqr(a) = sqr(b) + sqr(c) - 2 bc cos(A).

And I think you need the cosine rule to get home. The sine rule will give you your distance to the landmark. So you can draw a triangle CLH where C is your current location, L is the landmark and H is home, and you know the distance CL and LH and the angle at L. But the sine rule can't help you because the angle you know isn't opposite to any of the sides you know. You have to use cosine rule instead. Which means doing squares, square roots, additions and subtractions as well as memorising the cosine table (or knowing how to derive it from the sine table).

Alternative, you can draw a scale drawing. If you have enough information to do the maths you have enough to draw the triangles, and then you can measure the answer with a ruler.

You guys keep teaching me fun new stuff.

Thanks!

OK, so continuing my scenario where we have points:
L=Landmark
A=Current location #1
B=Current Location #2
H=Home

Originally I had taken a bearing of 332 from A to L, then hiked on a bearing of 33 degrees for 1.5 miles to B. Then I took a bearing of 301 degrees from B to L.

From that information, using the Law of Sines I was able to figure out that the defined triangle is:

Point--Angle--OppSideLength
L--31 degrees--1.5 miles
A--61 degrees--2.55 miles
B--88 degrees--2.91 miles

Now the new stuff using the Law of Cosines:
Suppose I know that the bearing from L to Home is 262 degrees and the distance from L to H is 2.566 miles. My goal is to determine the bearing and distance from B to H in order to return home from current location #2.

First I determine the angle between sides LB and LH:
180 - (360-301) - [180 - (360-262)] = 39 degrees

As mentioned, there isn't enough info to use the Law of Sines. Now I can use the Law of Cosines:

BH = SQRT[ 2.566^2 + 2.55^2 - 2(2.566)(2.55) Cos(39) ]
BH = 1.708 miles

Then I use the Law of Sines to find the other angles:
1.708/Sin(39) = 2.566/Sin(B)

Angle at B = ArcSin[(2.566/1.708)Sin(39)] = 71 degrees

Angle at H = 180 - 39 - 71 = 70 degrees

The bearing from B to H is 33+88+71 - 180 = 12 degrees

So, to get home from B I need to travel on a bearing of 12 degrees for 1.7 miles.

Drawing pictures helps me a lot with this stuff.

Very cool!! Thanks again for making my brain work a bit more than it usually would on a day off.

Ken K.

Yes my watch has only the C & D scales and also a time scale.
I use it a lot through out the day, I feel naked without it <img src="/images/graemlins/smile.gif" alt="" /> There are some things that slide rules seem to do better than calculators or spreadsheets.
I didnt use them at school, but two of my older brothers did.
One of my friends is a pilot and he has a Jeppesen E6-B and after having a play with it I bought one. Then I bought a smaller pocket sized Jeppesen CR-5 (these are Australian prices so this week you need to line up 73 on the C scale with 10 on the D scale to convert into US dollars <img src="/images/graemlins/smile.gif" alt="" /> )
I also picked up an old Aristo and a Sun Hemma normal type slide rules from a second hand shop for a few dollars each. Both of these have the Trig scales.
Both the Jeppesen's have a Wind triangle calculator on the back side, so I guess with a bit of experimenting you could work out how to do it on the back.

> So, to get home from B I need to travel on a bearing of 12 degrees for 1.7 miles.

Looks good to me. Did you figure it all out just from being told the cosine formula? Kudos if so.

The short version:

1. Took a bearing on Landmark from postion A
2. Walked from A to B
3. Took another bearning on Landmark from position B
4. Use Law of Sines to determine all angles and side lengths for LAB triangle.
5. Using info from #4, bearing & distance from Landmark to Home, AND Law of Cosines to determine distance from B to Home.
6. Use Law of Sines to find all angles & sides for LBH triangle. This gives bearing from B to Home.

This couldn't have been done without both laws.

I honestly can't imagine doing this in the field without a decent piece of paper and a scientific calculator.