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Bot GPT 3.5 To find the length of f, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all sides and their opposite angles.
Applying the Law of Sines to angle E, we have:
f/sin(E) = g/sin(G)
Substituting the given values, we have:
f/sin(25°) = 8.4/sin(79°)
Rearranging the equation to solve for f, we have:
f = (sin(25°) * 8.4) / sin(79°)
Using a calculator, we find:
f ≈ (0.4236 * 8.4) / 0.9823 ≈ 3.6192 / 0.9823 ≈ 3.6867
Therefore, the length of f is approximately 3.7 inches (to the nearest tenth of an inch).