To find the length of side EF in triangle DEF, we can use the trigonometric functions related to right triangles.
Given:
- Angle D = 40°
- Side DE (adjacent to angle D) = 7.6 units
- Angle E is the right angle
Since we want to find side EF (which is opposite angle D), we can use the tangent function:
\[ \tan(D) = \frac{\text{opposite}}{\text{adjacent}} \]
Here, the opposite side is EF, and the adjacent side is DE. Thus, we have:
\[ \tan(40°) = \frac{EF}{7.6} \]
To solve for EF, we rearrange the equation:
\[ EF = 7.6 \cdot \tan(40°) \]
Next, we calculate \(\tan(40°)\):
\[ \tan(40°) \approx 0.8391 \]
Now, we can substitute this value into our equation:
\[ EF = 7.6 \cdot 0.8391 \approx 6.38 \text{ units} \]
Thus, the measure of side EF, rounded to the nearest hundredth, is:
\[ \boxed{6.38 \text{ units}} \]
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