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I-C #8.29 #4.13 and #4.30

 
 
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I-C #8.29 #4.13 and #4.30
by Christine Wang - Thursday, February 17, 2022, 5:34 PM
 

I don't really understand these questions, like how to graph them.

 
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Re: I-C #8.29 #4.13 and #4.30
by John Lensmire - Friday, February 18, 2022, 10:37 AM
 

Let's start with 8.29. We have a cube ABCD-EFGH. The important part of this labeling is that ABCD is one face (the bottom face below) while EFGH is the other face, with E "above" A, F "above B, etc.


This gives tetrahedron ACFH as in the picture below:


The key for then finding the volume is noting that we can create this tetrahedron by removing 4 triangular pyramids from the outside. For example, ABC-F from the front.

Hope this helps visualize a little bit! Note you can click either image above for a larger picture.

For the others, is chapter 4 correct? Chapter 4 Q13 and Chapter 4 Q30? I'm happy to give some additional tips for those, just wanted to confirm the questions.

 
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Re: I-C #8.29 #4.13 and #4.30
by Christine Wang - Friday, February 18, 2022, 11:40 AM
 

Thank you so much! For the other questions, you got them. Sorry I forgot to add this question in the first comment, but can you also explain 1.17? Thank you.

 
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Re: I-C #8.29 #4.13 and #4.30
by John Lensmire - Friday, February 18, 2022, 12:59 PM
 

For 1.17, remember the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

For 4.13, note that the values of the trig. functions only depend on the ratios between the sides. So based on the information (remember tangent is opposite / adjacent) we get assume that we have the following triangle:


For 4.30, the following (slightly messy) drawing hopefully helps:


What can you say about tan(55) and tan(75) in terms of x and y?

 
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