SAT Math Multiple Choice Practice Question 17: Answer and Explanation

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Question: 17


In this diagram, the measure of side j is

A. 7
D. 14

Correct Answer: A


A. To answer this question, you must first realize that the triangles here are special; break up the 75° angle at the bottom right into a 45° angle and a 30° angle. The top right triangle is a 45-45-90 triangle, which makes both of its legs equal to 14. The bottom leg is also the hypotenuse of the 30-60-90 triangle at the bottom. In a 30-60-90 triangle, the hypotenuse must be twice the shortest leg, which is j. Therefore, j equals 7.

Don't remember the special triangle ratios you need to know for this problem? Well, don't panic. They're at the top of each mathematics section of the SAT, so take a quick peek at the directions at the beginning of the section to refresh your memory.

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