Question

find j. write your answer in simplest radical form. centimeters

Explanation:

Step1: Identify the triangle type

This is a 30 - 60 - 90 right - triangle. In a 30 - 60 - 90 triangle, if the hypotenuse $c$ is given and we want to find the side opposite the 30° angle $a$, the relationship is $a=\frac{c}{2}$, and the side opposite the 60° angle $b = a\sqrt{3}$. Here, the hypotenuse $c = 6$ cm.

Step2: Determine the value of $j$

The side $j$ is opposite the 30° angle. Using the ratio of sides in a 30 - 60 - 90 triangle, if the hypotenuse $c = 6$ cm, then the side opposite the 30° angle $j=\frac{6}{2}\sqrt{3}$.
$j = 3\sqrt{3}$ cm

Answer:

$3\sqrt{3}$