Thank you for the opportunity to help you with your question!
The trick to this problem is that the triangle formed by the man and his shadow is a similar triangle to the triangle from the tree to the end of the shadow. Since the two triangles are similar, their sides are proportional. Therefore the bases of the triangles can be compared as well as the heights. Algebraically, this means that x/8 = 20/5.
Solving for x:
x/8 = 20/5
simplify the tright hand side
x/8 = 4
Multiply both sdes by 8
x = 32
Now it asked the distance from the man to the tree, but x is the distance from the end of the shadow to the man. To get the distance to the tree, subtract the length of the shadow. 32 - 8 = 24.
The man is 24 feet from the tree.
Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 28th, 2015
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