Question

12 mark for review
triangle fgh is similar to triangle jkl, where angle f corresponds to angle j and angles g and k are right angles. if \\(\sin(f) = \frac{308}{317}\\), what is the value of \\(\sin(j)\\)?
a \\(\frac{75}{317}\\)
b \\(\frac{308}{317}\\)
c \\(\frac{317}{308}\\)
d \\(\frac{317}{75}\\)

Explanation:

Step1: Recall Similar Triangles Property

Similar triangles have corresponding angles equal. So, angle \( F \) and angle \( J \) are equal (since \( \triangle FGH \sim \triangle JKL \) and \( F \) corresponds to \( J \)).

Step2: Recall Sine of Equal Angles

If two angles are equal, their sine values are equal. Since \( \angle F=\angle J \), then \( \sin(F)=\sin(J) \).

Step3: Substitute the Given Value

We know \( \sin(F)=\frac{308}{317} \), so \( \sin(J)=\frac{308}{317} \).

Answer:

B. \(\frac{308}{317}\)