Final answer:
The extensor hallucis longus muscle is responsible for extending the big toe. It's located in the anterior compartment of the leg and contrasts with the tibialis anterior, gastrocnemius, and soleus, which serve different functions.
Step-by-step explanation:
The muscle that extends the big toe is the extensor hallucis longus. This muscle is located in the anterior compartment of the leg and is responsible for dorsiflexion of the foot at the ankle and extension of the big toe. It lies deep to the tibialis anterior and extensor digitorum longus muscles. The other muscles listed have different functions: Tibialis anterior is involved in dorsiflexion and inversion of the foot, Gastrocnemius contributes to plantar flexion of the foot at the ankle when the knee is extended, and Soleus is also involved in plantar flexion but mainly when the knee is flexed.