The use of self-avatars is gaining popularity thanks to affordable VR headsets. Unfortunately, mainstream VR devices often use a small number of trackers and provide low-accuracy animations. Previous studies have shown that the Sense of Embodiment, and in particular the Sense of Agency, depends on the extent to which the avatar's movements mimic the user's movements. However, few works study such effect for tasks requiring a precise interaction with the environment, i.e., tasks that require accurate manipulation, precise foot stepping, or correct body poses. In these cases, users are likely to notice inconsistencies between their self-avatars and their actual pose. In this paper, we study the impact of the animation fidelity of the user avatar on a variety of tasks that focus on arm movement, leg movement and body posture. We compare three different animation techniques: two of them using Inverse Kinematics to reconstruct the pose from sparse input (6 trackers), and a third one using a professional motion capture system with 17 inertial sensors. We evaluate these animation techniques both quantitatively (completion time, unintentional collisions, pose accuracy) and qualitatively (Sense of Embodiment). Our results show that the animation quality affects the Sense of Embodiment. Inertial-based MoCap performs significantly better in mimicking body poses. Surprisingly, IK-based solutions using fewer sensors outperformed MoCap in tasks requiring accurate positioning, which we attribute to the higher latency and the positional drift that causes errors at the end-effectors, which are more noticeable in contact areas such as the feet.