Question
From a point on the ground, the angle of elevation to the top of a tree is 30 degrees. If you walk 20 feet closer to the tree, the angle of elevation becomes 45 degrees. What is the height of the tree?
Solution
Let the height of the tree be h feet. Let the initial distance from the point on the ground to the tree be x feet. From the first angle of elevation, we have tan(30) = h/x From the second angle of elevation, we have tan(45) = h/(x - 20) Since tan(45) = 1, we have 1 = h/(x - 20), so h = x – 20 Substituting h into the first equation: tan(30) = (x - 20)/x -Constable/1726830769-127.JPG)
Answer: (b)
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