find the value of variable x. if your answer is not an integer, write it in simplest radical form with the…

find the value of variable x. if your answer is not an integer, write it in simplest radical form with the denominator rationalized.\nx = \n(simplify your answer. type an integer or a simplified fraction.)

find the value of variable x. if your answer is not an integer, write it in simplest radical form with the denominator rationalized.\nx = \n(simplify your answer. type an integer or a simplified fraction.)

Answer

Explanation:

Step 1: Identify triangle type

30-60-90 right triangle with angles 30°, 60°, 90°.

Step 2: Apply side ratio

Sides ratio: 1 (30° opposite) : √3 (60° opposite) : 2 (hypotenuse). Let x be 30° opposite side, 60° opposite side is 7 = x√3.

Step 3: Solve for x

x = 7 / √3, rationalize denominator: x = (7√3) / 3.

Answer:

$\frac{7\sqrt{3}}{3}$