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　　Read the following SAT test question and then click on a button to select your answer.

　　Miguel is 180centimeters tall. At 2:00 p.m. one day, his shadow is 60 entimeters long, and the shadow of a nearby fence post is t centimeters long. In terms of t what is the height, in centimeters, of the fence post?

　　(A) t+120

　　(B) t/3

　　(C) 3t

　　(D) 4

　　(E) (t/3

　　Explanation

　　The situation described in the question can be pictured as in the figure below, where x s the height, in centimeters, of the fence post.There are two right triangles in the figure. One triangle is formed by part of the line from the sun to point p

　　, the perpendicular from Miguel’s head to the ground, and Miguel’s shadow along the ground. The other triangle is formed by part of the line from the sun to point , the perpendicular from the top of the fence post to the ground, and the fence post’s shadow along the ground. Since these two right triangles share the acute angle at , they are similar triangles. Since the corresponding sides of similar triangles are in proportion, it follows that. Solving this equation for , the height, in centimeters, of the fence post, yields x=3t

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