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Finding a Distance X : Triangles and Circles

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In the problem I am being asked to solve for the value of X. I have tried setting up right triangles and a mix of right and oblique triangles but have not been able to get the right combination. The value of A is 3.5 and the answer of X is 1.8376. The book gives the answer and we construct the problem.

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A distance is found using trigonometric relations.

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