Question

due on 09.10.2025 not graded directions 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. select the correct answer 4√3 4√6 8 2

Explanation:

Step1: Analyze left - hand right - triangle

In the left - hand right - triangle with an angle of $60^{\circ}$ and the side adjacent to the $60^{\circ}$ angle equal to 4. Using the tangent function $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, $\tan60^{\circ}=\sqrt{3}=\frac{\text{opposite}}{4}$, so the opposite side is $4\sqrt{3}$. Using the cosine function $\cos60^{\circ}=\frac{1}{2}=\frac{4}{\text{hypotenuse}}$, the hypotenuse of the left - hand right - triangle is 8.

Step2: Analyze right - hand right - triangle

The right - hand right - triangle is a $45 - 45-90$ triangle. The side that is the hypotenuse of the left - hand right - triangle serves as a leg of the right - hand right - triangle. In a $45 - 45-90$ triangle, if the leg length is $a$, the hypotenuse is $a\sqrt{2}$. Here, if $a = 8$, the hypotenuse of the right - hand right - triangle is $8\sqrt{2}$. The possible side - lengths we can get from the figure are 4, $4\sqrt{3}$, 8.

Answer:

$4\sqrt{6}$