Question

find j.
right triangle with right angle, one leg 2√2 ft, angle 60°, other angle 30°, side j opposite 60°? wait, no, the triangle has right angle, one leg 2√2 ft, angle at that vertex 60°, angle at the bottom 30°, side j is one of the legs? wait, the image shows a right triangle with right angle, one leg (adjacent to 60°) is 2√2 ft, angle 60°, angle 30°, and side j. then: write your answer in simplest radical form. blank feet. submit

Explanation:

Step1: Identify triangle type

This is a 30 - 60 - 90 right triangle. In a 30 - 60 - 90 triangle, the sides are in the ratio $1:\sqrt{3}:2$, where the side opposite 30° is the shortest, opposite 60° is $\sqrt{3}$ times the shortest, and the hypotenuse is twice the shortest. Also, we can use trigonometric ratios. Let's use tangent. $\tan(60^{\circ})=\frac{j}{2\sqrt{2}}$.

Step2: Recall $\tan(60^{\circ})$ value

We know that $\tan(60^{\circ}) = \sqrt{3}$. So, $\sqrt{3}=\frac{j}{2\sqrt{2}}$.

Step3: Solve for j

Multiply both sides by $2\sqrt{2}$: $j = 2\sqrt{2}\times\sqrt{3}$. Using the property $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$, we get $j = 2\sqrt{6}$.

Answer:

$2\sqrt{6}$