In $\triangle V W X$, the measure of $\angle X=90^{\circ}, V X=45, W V=53$, and $X W=28$. What is the value of the tangent of $\angle V$ to the nearest hundredth?
Answer:

Step 1 ：In right triangle \(\triangle VWX\), where \(\angle X=90^\circ\), the lengths of the sides are given as \(VX=45\), \(WV=53\), and \(XW=28\). We are asked to find the value of the tangent of \(\angle V\).

Step 2 ：In a right triangle, the tangent of an angle is equal to the ratio of the side opposite to the angle to the side adjacent to the angle.

Step 3 ：Here, the side opposite to \(\angle V\) is \(XW\) and the side adjacent to \(\angle V\) is \(VX\). So, we can calculate the tangent of \(\angle V\) as \(\frac{XW}{VX}\).

Step 4 ：Substituting the given values, we get \(\frac{XW}{VX} = \frac{28}{45}\).

Step 5 ：Calculating the above expression, we get the value of the tangent of \(\angle V\) to be approximately 0.62.

Step 6 ：Final Answer: The value of the tangent of \(\angle V\) to the nearest hundredth is \(\boxed{0.62}\).