Digital PSAT Math Practice Question 206: Answer and Explanation

Question: 206

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 it is that this is asking for what the tangent of angle A would be, which is the opposite side over the adjacent, giving you .