1. **Problem statement:** We are given that Rory's shot length is 187 m, and we need to find the angle $ |\angle FTP| $ by which his shot is off target, rounded to the nearest degree. 2. **Understanding the problem:** The angle $ |\angle FTP| $ represents the deviation of the shot from the intended target direction. We assume the intended target distance is known or can be derived from the problem context (not provided here), but since only the actual length is given, we interpret this as finding the angle between the actual shot vector and the target vector. 3. **Formula used:** To find the angle between two vectors when their lengths and the length of the resultant vector are known, we use the Law of Cosines: $$ c^2 = a^2 + b^2 - 2ab \cos(C) $$ where $a$ and $b$ are the lengths of the two sides, $c$ is the length of the resultant side, and $C$ is the angle opposite side $c$. 4. **Applying the formula:** Let $a$ be the intended shot length, $b = 187$ m the actual shot length, and $c$ the distance between the target and the actual shot endpoint. Since the problem does not provide $a$ or $c$, we assume the intended length $a$ is known or equal to the target distance. Without this, the problem cannot be solved numerically. 5. **Assuming intended length $a = 200$ m (example):** $$ 187^2 = 200^2 + c^2 - 2 \times 200 \times c \times \cos(\theta) $$ Since $c$ is unknown, this cannot be solved directly without more data. 6. **Conclusion:** The problem as stated lacks sufficient data to calculate $ |\angle FTP| $. Please provide the intended shot length or the distance between the target and the actual shot endpoint. **Note:** If the intended length is the straight line from F to T, and the actual shot length is 187 m, then the angle $ |\angle FTP| $ can be found by: $$ \cos(\theta) = \frac{\text{intended length}}{187} $$ and then $$ \theta = \arccos\left(\frac{\text{intended length}}{187}\right) $$ rounded to the nearest degree. Since the intended length is not given, the problem cannot be solved numerically here.