In this figure, sin(a) = 2/3
What is the value of cos(b) ?

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  C)  2/3

Step-by-step explanation:

In order to answer the question, we must make an assumption about the given figure. We must assume it is a rectangle, so the left side and right side of the figure are the same length.

The ratio of the right side of the figure to the diagonal is sin(a). The ratio of the left side of the figure to the diagonal is cos(b). If we assume that the left and right sides are the same length, then ...

  sin(a) = 2/3 = side/diagonal = cos(b) = 2/3

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Additional comments

The figure does not have enough information to support our assumption. Of the answer choices, only (A) is a reasonable alternative. (The value of the cosine must be at most 1.)

The first attachment shows the figure with sin(a) = cos(b) = 2/3. The second attachment shows the figure with cos(b) = 1/3. There is nothing in the given drawing to say this is an incorrect interpretation. (Drawings cannot be assumed to be to scale.)