Solving for angle
- Thread starter Uncus
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Please demonstrate your efforts. It may help to designate which rays (starting at the Origin) actually belong to the same line.
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mmm4444bot
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Who gave you this diagram?
Were you asked to express X in terms of Y and/or Z?
Please post the complete text of the exercise, including the instructions. We would like also for you to familiarize yourself with the forum's basic guidelines. Thank you! :cool:
Were you asked to express X in terms of Y and/or Z?
Please post the complete text of the exercise, including the instructions. We would like also for you to familiarize yourself with the forum's basic guidelines. Thank you! :cool:
Steven G
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You can set up a system of equations and see if that will help (Hint: it won't but TRY anyways!)
I drew this diagram. These angles are shapes of a petrous temporal bone of the skull for research purposes. My goal is to calculate X using the two known angles. I have a list of 100 sets of angles that I need to convert if possible, which will save me a tremendous amount of time rather than going back and re-measuring all of them.
My work so far:
180 = 146 + z - x. --> z - x = 34
90 = y + X + 24 --> x + y = 66
360 = 170 + y + z + 90 --> y + z = 100
After this I wasn't able to continue to solve for x. I'm assuming that this is not solvable but before I give up I wanted to see if I am missing a theorem that might be able to solve it.
Thanks!
My work so far:
180 = 146 + z - x. --> z - x = 34
90 = y + X + 24 --> x + y = 66
360 = 170 + y + z + 90 --> y + z = 100
After this I wasn't able to continue to solve for x. I'm assuming that this is not solvable but before I give up I wanted to see if I am missing a theorem that might be able to solve it.
Thanks!
Steven G
Elite Member
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- Dec 30, 2014
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- 14,379
Yep, that is as far as I got. The 3rd equation is the sum of the 1st and 2nd. That is, you do not have three independent equations.
mmm4444bot
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Correct -- a numerical solution is not possible. X would need to be expressed in terms of Y or Z.
Visualize the rays forming the 24° angle rotating about the vertex a bit (one direction or the other). As the 24° angle's position fluctuates in QIII, either X shrinks a bit and Y grows by the same amount or vice versa.
Yet, X + 24° + Y remains 90°. So there's not enough information to determine either X or Y. Many possibilities.