PSAT Math Multiple-Choice Question 248: Answer and Explanation

Question: 248

When New York City built its 34th Street subway station, which has multiple underground levels, it built an elevator that runs along a diagonal track approximately 170 feet long to connect the upper and lower levels. The angle formed between the elevator track and the bottom level is just under 30 degrees. What is the approximate vertical distance in feet between the upper and lower levels of the subway station?

• A. 85
• B. 98
• C. 120
• D. 147

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Additional Topics in Math/Geometry

Getting to the Answer: Organize information as you read the question. Here, you'll definitely want to draw and label a sketch.

The lower level, the vertical distance between levels, and the diagonal elevator track form a 30-60-90 triangle, where the elevator track is the hypotenuse. The vertical distance is opposite the 30° angle so it is the shortest leg. The rules for 30-60-90 triangles state that the shortest leg is half the length of the hypotenuse, so the vertical distance between levels is approximately 170 ÷ 2 = 85 feet, (A).