To find the value of \( \tan J \) for triangle HIJ, we can use the properties of similar triangles. In similar right triangles, the corresponding ratios of the lengths of the sides are equal.
If we denote the angle \( J \), the relationship between \( \tan J \) can be expressed as:
\[ \tan J = \frac{\text{opposite side}}{\text{adjacent side}} \]
Assuming you have the lengths of the sides of triangle HIJ or any given relevant information from triangle EFG, you can substitute those values in to calculate \( \tan J \).
If you're provided with the lengths of the triangle sides or a specific image for reference, I can help further with those values. Since they are similar triangles, finding \( \tan J \) should follow directly from the lengths of HIJ:
- If the opposite side to angle J is \( a \) and the adjacent side is \( b \), then:
\[ \tan J = \frac{a}{b} \]
If you could provide the necessary values or clarify the choices A, B, C, or D, I'd be able to assist you with finding the correct answer.
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