1. **State the problem:** We need to find the cotangent of angle $W$ in the right triangle $WVX$ where $WV=10$, $VX=24$, and hypotenuse $WX=26$. 2. **Recall the definition:** In a right triangle, $\cot(\theta) = \frac{\text{adjacent side}}{\text{opposite side}}$ for angle $\theta$. 3. **Identify sides relative to angle $W$:** - The side adjacent to angle $W$ is $WV = 10$ (vertical side). - The side opposite to angle $W$ is $VX = 24$ (horizontal side). 4. **Apply the formula:** $$\cot(W) = \frac{WV}{VX} = \frac{10}{24}$$ 5. **Simplify the fraction:** $$\cot(W) = \frac{\cancel{10}}{\cancel{24}} = \frac{5}{12}$$ 6. **Final answer:** $$\cot(W) = \frac{5}{12}$$