The elegant construction of an auxiliary equilateral triangle turns a messy figure into a lesson in geometric intuition. It’s a refreshing reminder that the right perspective is often more powerful than brute-force calculation.
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Can you find the length X?Added:
Can you find the length x?
Here If we extend AD and BC Suppose this point is P.
Then in the angle ABP It is A B P This angle is 60° This angle is 60° That means this angle It will be also 60° So AP AB and BP They will be equal.
And AB is 34 So BP It will be also 34 and AP It will be also 34 We get BP is 34 And this angle is 60° and Now CP is BP minus BC and BP is 34 minus BC is 10 that will be 24 CP is 24 and now in triangle CPD it is C P D This angle is 90° This angle is 90° and this angle is 60° CP is 24 CD is X So X It will be CP times sine 60° and CP is 24 and sine 60° is root three over two that will be 12 root three So X is 12 root three >> [music]
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