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In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

You're locked out of your house. the only open window is on the second floor, 25 feet above the ground. there are bushes along the edge of the house, so you will need to place the ladder 10 feet from the house. what length ladder do you need to reach the window?

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle