This is a question from Engineering Mechanics by Shames. I am unable to resolve this as the question mentioned.
2$\begingroup$ So what have you considered? What was covered in the chapter? $\endgroup$– Solar MikeFeb 10, 2022 at 4:12
$\begingroup$ please think of a question to ask and add it to your post $\endgroup$– jsotolaFeb 10, 2022 at 5:06
$\begingroup$ We will, or at least should not just give you answers to homework questions. If you post your best efforts, we may help you find your errors. $\endgroup$– Eric SFeb 10, 2022 at 16:58
$\begingroup$ Welcome to Engineering! This looks like a homework question. In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? Please edit your question to include this information. $\endgroup$– Wasabi ♦Feb 11, 2022 at 2:34
This questions appears to be about essentially vectors. If you recall a vector has two components: Magnitude and Direction. In this question, you are asked to take the magnitude of the 100 lbf and break it into components of two other vectors. One vector is going to be vertical up, and the other vector is going to be up and to the the right at an angle 20 degrees from the horizontal.
You may recall that the sum of component vectors will equal that of the resultant. So if you place the component vectors tip to tail, you will wind up creating a triangle. Using the angles supplied in the question, you can then use trigonometry to determine the magnitude of the component vectors. Depending on the degree of accuracy you need, you can draw this out to scale and measure as an alternate means of finding the solution or at worst seeing if your answers are in the right ball park.
I did the following in AutoCAD to illustrate the graphical approach without giving you the answer. The mathematical approach will be to use trig to solve for A and B.