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