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Slid Trigonometry : Type II Pyramid

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This triangular pyramid is a type II as the book puts it. Three faces are right triangles and the 4th in a diagonal plane is an oblique triangle. The book explaines that if the angle to be found is in the oblique triangle you should solve for an auxilliary angle in the third right angle which lies at the same vertex as the required angle, thus spliting the pyramid into two parts. I need help constructing the auxilliary angle.
The problem is to solve Beta with one face angle at 25 degrees and Theta which is 22 degrees.

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An auxilliary angle in a type II pyramid is calculated.

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I am in need of help in construction and solving this problem. I am in an independent study program. This triangular pyramid is a type II as the book puts it. 3 faces are right triangles and the 4th in a diagonal plane is an ...

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  • 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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