The Geometry of Banking a basket
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mateoballislife
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The Geometry of Banking a basket
I am having trouble with step 3 of the procedure and am having a hard time trying to find X1 and X2 when I know Xtot, Ytot, Y1, and Y2.
Re: The Geometry of Banking a basket
Hello. This is an interesting project. I can understand your frustration. There are lot of possibilities of equations to ponder and determine which one will get you to the answer!
The key is the phrase "Since the angle of incidence is equal to the angle of reflection, these two triangles are similar." They are referring to the blue and green triangles being similar, meaning the angular value of alpha is the same for both brown two-sided arrows in Figure 9.
Because those values are the same, the complimentary angles inside the blue and green triangles are also equal. That makes the blue and green triangles proportional. Let's define the complimentary angle as (90-alpha).
Using a little SOH CAH TOA, can you come up with equations for both the blue and green triangles in the form of (90-alpha), Y1, Y2, X1, X2? Once you do this, you should see that with a little substitution, you can generate an equation in the form of only Y1, Y2, X1, and Xtot. Then, it is just a matter of rearranging the equation to express it in the form of X1 = ...
Give this a shot and write back if you have further questions.
Good luck!
The key is the phrase "Since the angle of incidence is equal to the angle of reflection, these two triangles are similar." They are referring to the blue and green triangles being similar, meaning the angular value of alpha is the same for both brown two-sided arrows in Figure 9.
Because those values are the same, the complimentary angles inside the blue and green triangles are also equal. That makes the blue and green triangles proportional. Let's define the complimentary angle as (90-alpha).
Using a little SOH CAH TOA, can you come up with equations for both the blue and green triangles in the form of (90-alpha), Y1, Y2, X1, X2? Once you do this, you should see that with a little substitution, you can generate an equation in the form of only Y1, Y2, X1, and Xtot. Then, it is just a matter of rearranging the equation to express it in the form of X1 = ...
Give this a shot and write back if you have further questions.
Good luck!
Deana