Find the length of side x in simplest radical form with a rational denominator.

Step-by-step explanation:

In all 30-60-90 triangles, the side lengths are in the ratio , where is the side opposite to the 30 degree angle and is the hypotenuse of the triangle. Since the side opposite to the 30 degree angle is marked as 3, the value of must be .

Alternatively, we can use basic trig. for a right triangle to solve. In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Thus, we have:

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.

lo.lll

step-by-step explanation: