Question

answer the question below to check your understanding and move forward in the course! this quiz is not graded. choose the answer that is not a side length for the following image. youll get it right next time! $4\sqrt{3}$ $4\sqrt{6}$ 8 2 answer feedback review your ratios of the 30 - 60 - 90 triangles. retry

Explanation:

Step1: Analyze 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the side opposite the 30 - degree angle is $a$, the side opposite the 60 - degree angle is $a\sqrt{3}$ and the hypotenuse is $2a$. Given one side is 4. If 4 is the side opposite the 30 - degree angle, then the side opposite the 60 - degree angle is $4\sqrt{3}$ and the hypotenuse is 8.

Step2: Consider other triangle properties

There is no geometric relationship within the given figure that would result in the side - length $4\sqrt{6}$. A 45 - 45 - 90 triangle (if present) has side ratios of $1:1:\sqrt{2}$, and it doesn't lead to $4\sqrt{6}$ either.

Answer:

$4\sqrt{6}$