I would begin by sketching the problem. By doing that, I hope that you can see that the tree and its linear shadow along the ground form two legs of a right triangle.
Similarly, the pole and its linear shadow along the ground form two legs of a second right triangle.
These two triangles are SIMILAR, because the sun is in the same place casting a shadow at the same angle in each case and, of course, they both have a right angle.
Thus, I would set up a proportion to solve for the unknown height of the pole, which I will call P. For proportion to be true, you need to be using the same units for corresponding lengths and heights, which is not a problem in this case.
Height of pole Height of tree
_____________________ = _______________________
Length of pole's shadow Length of tree's shadow
P 91
______ = _______
24 135
You have to love cross-multiplying to solve proportions.
(24)(91) = 135P
2184 = 135P
2184 135P
_____ = ______
135 135
P is 16.2 to the nearest tenth of a foot, meaning the height of the pole is approximately 16.2 feet.
