Algebra-2

In the provided diagram, we have a right triangle with the right angle at point B. The lengths of the sides are as follows: the side AB opposite to angle C has a length of 9, and the side CB adjacent to angle C has a length of 3. Our objective is to find the tangent value of angle C.

In a right triangle, the tangent (tan) of an angle is defined as the ratio of the side opposite to the angle to the side adjacent to the angle. In this case, for angle C, the side opposite the angle is AB with a length of 9, and the side adjacent to the angle is CB with a length of 3.

Therefore, the tangent of angle C can be calculated as follows:

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