The length of r, to the nearest 10th of an inch, is 2.4 inches.
The relationship between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it states that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.
Given that in ΔQRS, s = 5.2 inches, ∠S=129° and ∠Q=30°. The value of side r will be calculated by using the sin angle theorem.
The value of r is,
r / sin21 = s / sin129
r = 5.2 x ( sin21/sin129)
r = 5.2 x 0.46
r = 2.4 inch
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