How Does a Tassel's Angle Reveal a Car's Acceleration?

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Your friend's 10.9-g graduation tassel hangs on a string from his rear-view mirror. When he accelerates from a stop light, the tassel deflects backward toward the rear of the car. If the tassel hangs at an angle of 5.60° relative to the vertical, what is the acceleration of the car?


I realize this isn't difficult. I think I'm making it more complicated than it needs to be because I'm not sure how to start/ which equations to use. There's acceleration in both directions so I need to set up the x and y components of the acceleration/force but beyond that I'm lost. Any help with setting it up/ and or solving it would be much appreciated! I would rather you show the steps to solve it than the answer if at all possible. Thank you so much!
 
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Welcome to PF.

Consider that acceleration is a vector too.

If the tassel is being pulled radially, then you have a right triangle where g is the vertical, and a of car is the horizontal.

Consider then tan-1 of the sides?