PSAT Math Grid-Ins Question 124: Answer and Explanation

Question: 124

In a certain right triangle, the sine of angle A is and the cosine of angle A is .

What is the ratio of the smallest side of the triangle to the median side of the triangle?

Correct Answer: 5/12

Explanation:

The triangle as described looks like this:

Given this sine and cosine, the triangle will be a multiple of the special right triangle 5-12-13. The smallest side is 5, and the median side is 12. So the ratio of the smallest side of the triangle to the median side of the triangle is .

Another way to think about the answer is to realize that the question is asking for the tangent of angle A. The tangent is the opposite side over the adjacent side, which is .