Multiple choice

In a $30-60-90$ triangle, the length of the hypotenuse is 6. What is the length of the shortest side?

  1. $2$
  2. $3$
  3. $3 \sqrt{2}$
  4. $3 \sqrt{3}$
  5. $6 \sqrt{2}$
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B Correct answer
Explanation

In a 30-60-90 triangle, the sides are in the ratio 1 : sqrt(3) : 2. The hypotenuse is 2x = 6, so x = 3. The shortest side is x = 3.

AI explanation

In a 30-60-90 triangle, the ratio of the side lengths is 1, sqrt(3), and 2. The side opposite the 30-degree angle is the shortest side, and its length is exactly half the length of the hypotenuse. Since the hypotenuse is given as 6, dividing by 2 gives the shortest side as 3.

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