If segment FD = 30 units and segment FE = 55 units, what is the value of a? Round the solution to the nearest hundredth.

In triangle DEF, which has a right angle at F, we can use the information given about the segments and the properties of a right triangle to find the angles.

You specified that FD = 30 units and FE = 55 units. To find the angle D (which is angle a) in triangle DEF, we can use the trigonometric functions. First, let's use the tangent function:

\[
\tan(a) = \frac{\text{opposite}}{\text{adjacent}} = \frac{FE}{FD}
\]

Substituting the given lengths:

\[
\tan(a) = \frac{55}{30}
\]

Now, we can find the angle a by taking the arctangent (inverse tangent):

\[
a = \tan^{-1}\left(\frac{55}{30}\right)
\]

Calculating this value:

1. Compute the division:
\(\frac{55}{30} \approx 1.8333\)

2. Now find the inverse tangent:
\( a \approx \tan^{-1}(1.8333) \)

Using a calculator to find \( a \):

\[
a \approx 61.39^\circ
\]

Therefore, rounding to the nearest hundredth, the value of \( a \) is approximately **61.39** degrees.

So the answer is:

**61.39**.