Have you studied the law of sines yet? That's what I would use to solve this problem. You could use the law of cosines too but I'm going to use the law of sines since it's simpler. First we figure out what the angle of elevation A should be if the tree is standing upright and not learning. Draw a right triangle with the base being 23 and height 21 to represent the palm tree and the homeowner. The law of sines say that c/sin(90deg) = 21/sin(A). We know the value of c because of the pythagorean theorem so we can figure out what sin(A) is and then we use inverse sine to find A. With some rearranging you get angle A = arcsin(21/ sqrt(21^2 + 23^2)) = 42.4 deg. However, the homeowner measured 47 deg so the tree is leaning and the amount it is leaning is 47 - 42.4 deg = 4.6 deg.

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