Answer :
The value of D is 49.1º to the nearest degree using the law of sines.
To solve for angle D, we can use the law of sines, which states that for any triangle with sides a, b, and c opposite angles A, B, and C respectively:
a/sin(A) = b/sin(B) = c/sin(C)
Using this formula, we can solve for angle D:
sin(D)/d = sin(F)/f
sin(D) = (d/f) × sin(F)
sin(D) = (76/20) × sin(17º)
sin(D) = 0.7588
Taking the inverse sine of both sides, we get:
D = [tex]sin^{-1}[/tex] × (0.7588)
D = 49.1º (rounded to the nearest tenth of a degree)
The law of sines can have two possible solutions for an angle, depending on the triangle. However, in this case, since angle D is opposite the longer side (d), there is only one possible solution.
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