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Gage : Finding a Distance from a Diagram Containing Triangles and Circles

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I have tried setting up this problem using right triangles but have not been able to solve it correctly. This problem is not as simple as it looks. It cannot be assumed that the bottom of the circle is tangent to a line drawn across the bottom. Solving for that one triangle is part of the solution.

Theta is given as 20 degrees and the book supplies the answer as 0.69341. The answer is not 0.625.

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A distance in a gage is found using trigonometric formulas on triangles and circles. The solution is detailed and is correct.

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Solution. We draw a graph( See above). Now we will compute the value of x which is equal to the length of segment BF. ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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