# Math Help - Measuring distance using subtense method.

1. ## Measuring distance using subtense method.

cot(1degree23minutes12seconds) is the angle in a subtense bar method of measuring (computing) distance. The formula is d=b/2cot(1degree23minutes12seconds/2. or cot(1.38667degrees) My text uses this formula and gets a distance of 82.6341 cm. How did they do that? How does one use this formula and/or convert degrees to measurement?

2. ## Re: Measuring distance using subtense method.

Trig isn't one of my strong points, but I'll try to answer.

My text uses this formula and gets a distance of 82.6341 cm. How did they do that?

$d=\frac{b}{2}*cot(\frac{\theta}{2})$

$d=\frac{2}{2}cot({1.38667}{2})=82.6341 cm$

How does one use this formula and/or convert degrees to measurement?

You're trying to measure the distance d from point P to point Q. In order to do so, you place a bar of known length B such that point Q divides the length of the bar in half.

From the picture above, you can see that

$cot(\frac{\theta}{2})=\frac{d}{\frac{b}{2}}$

So

$d=\frac{b}{2}*cot(\frac{\theta}{2})$

I'm not sure if you were asking but to convert angles to decimal degrees it's simply

$\theta=1^{\circ} 23' 12''=\frac{degrees}{1}+\frac{minutes}{60}+\frac{se conds}{3600}$

3. ## Re: Measuring distance using subtense method.

downthesun01, Thank you for your response. Perhaps you can straighten me out. I input the equation into my TI-89 titanium using the equation you posted but my result is 41.3108. Your result is 82.6341 cm. There is something I am not getting right. Is it that my calculator is screwed up by not returning the cotangent as (1.386672) multiplied by (2/2) or am I unaware of something? I really cannot account for nor understand why my results are different than yours. I sure hope you get back to me because I am stuck.

4. ## Re: Measuring distance using subtense method.

downthesun01, I realize now what I was doing wrong. I was not dividing the cotangent by 2. Once I did that I got the same answer as you. One more thing though. In my text I have a similar problem. This problem has two cotangent angles. One each at the ends of distance. On your diagram ona at point P; in my text a similar distance line ending in point Q. The answer in the back of my book is 345.4 cm. The result for distance in my calculator is 86.3459. I am guessing the .345 is the answer they are lookong for. Does this mean the 86 is meters and the .345 is the centimeters? Sorry to ask such questions, but I am trying to truly know and understand what I am doing.