PSAT Math Grid-Ins Question 149: Answer and Explanation

Question: 149

What is the value of the smallest side in a right triangle with a hypotenuse of 8 and angles of 30 and 60 degrees?

Correct Answer: 4

Explanation:

4 You can see what the side lengths are of this particular triangle in the drawing below:

You can easily calculate these side lengths because this is a 30-60-90 triangle. So the side lengths can be expressed as x, , and 2x. (This formula is provided at the beginning of the math section.) The hypotenuse of 8 equals 2x, and the shortest side equals x. Do the calculations to find the length of the shortest side:

8 = 2x
x = 4

Alternatively, you can just recognize that ratio of the smallest side to the hypotenuse in a 30-60-90 triangle is 1:2. So the value of the smallest side in a right triangle with a hypotenuse of 8 is 4.