Find the given trigonometric function of the indicated angle using triangle ABC. tan A, where $$a = 5 , b = 23 , c = 29$$

Question

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We are looking to find $	an A$ given the side lengths $a$, $b$, and $c$ of triangle $ABC$. The definition of $	an A$ is $\frac{	ext{opposite}}{	ext{adjacent}}$, where $	ext{opposite}$ and $	ext{adjacent}$ refer to the side lengths of the triangle with respect to angle $A$.

Thus, we need to determine which side in triangle $ABC$ is opposite angle $A$ and which is adjacent. We know that side $a$ is opposite angle $A$, so we need to determine whether side $b$ or side $c$ is adjacent to angle $A$.

Recall that in a right triangle, the hypotenuse is always opposite the $90^{\circ}$ angle, and the other two sides are adjacent to the acute angles. Therefore, since $c$ is the hypotenuse of triangle $ABC$, and $\angle C$ is the $90^{\circ}$ angle, we know that sides $a$ and $b$ are adjacent to angles $A$ and $B$, respectively.

We can then use the definition of $	an A$ to get:

$$	an A = \frac{	ext{opposite}}{	ext{adjacent}} = \frac{a}{b} = \frac{5}{23}$$

Therefore, the answer is $\boxed{	ext{(D)}}$.

Find the Given Trigonometric Function of the Indicated Angle Using a=5,b=23,c=29a = 5 , b = 23 , c = 29a=5,b=23,c=29

Find the Given Trigonometric Function of the Indicated Angle Using $a = 5 , b = 23 , c = 29$