1. **State the problem:** We need to find the cotangent of angle $P$ in a right triangle $\triangle PQR$ where $PQ=16$, $RQ=30$, and $PR=34$. The right angle is at $Q$. 2. **Recall the definition of cotangent:** $$\cot(\theta) = \frac{\text{adjacent side}}{\text{opposite side}}$$ for angle $\theta$ in a right triangle. 3. **Identify sides relative to angle $P$:** - The side opposite angle $P$ is $RQ = 30$. - The side adjacent to angle $P$ is $PQ = 16$. 4. **Calculate cotangent of $P$:** $$\cot(P) = \frac{\text{adjacent}}{\text{opposite}} = \frac{16}{30}$$ 5. **Simplify the fraction:** $$\frac{16}{30} = \frac{\cancel{2} \times 8}{\cancel{2} \times 15} = \frac{8}{15}$$ 6. **Final answer:** $$\cot(P) = \frac{8}{15}$$