SAT Lines, angles, and triangles Practice Question 12 (Easy)

Question bank / Lines, angles, and triangles

Math · Geometry and TrigonometryEasy

At the same time of day, a $6$ -foot-tall person casts a shadow $4.5$ feet long and a tree casts a shadow $30$ feet long. The person and the tree are both standing vertically on level ground. What is the height, in feet, of the tree?

$22.5$

$36$

$40$

$45$

Show answer and explanation

Answer: C

The sun's rays form similar right triangles with the person and the tree, so heights are proportional to shadow lengths: $\frac{6}{4.5} = \frac{h}{30}$ . Then $h = 30 \cdot \frac{6}{4.5} = 40$ feet.

Choice A sets up the proportion upside down, computing $30 \cdot \frac{4.5}{6}$ .

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