Although Trikonasana (Triangle Pose) is considered a beginning standing pose, it offers a lifetime's worth of lessons. And positioning the head and neck is certainly high on many students' list of challenges.
When you're in Triangle, you may find that your neck feels overly tense or compressed. Or you may find that it's nearly impossible to turn your head to look up at your top hand. Usually these problems can be resolved by fine-tuning the position of your head, neck, and shoulders to bring them into optimal alignment. (If you have preexisting neck injuries or arthritis, though, you may need to make further modifications with the guidance of an experienced teacher, or consult a health care practitioner.)
But first, let's dispel the notion that your neck should feel relaxed in Trikonasana. Your head, after all, weighs around 12 pounds. With your spine parallel to the floor, the muscles on the top side of your neck have to contract to hold that weight in place against gravity. Ultimately, Trikonasana will strengthen these muscles, including the upper trapezius and levator scapula (which extend from the base of the skull and back of the neck down to the upper scapula) and sternocleidomastoid (from the top of the breastbone and inner collarbones to just behind the ears). But since a working, contracting muscle feels tight and tense, strengthening it may be uncomfortable. This is especially true if you came to Trikonasana with weak side-neck muscles—which is likely, since few of us spend time holding our heads sideways outside of yoga practice.
You can give these muscles a head start in the strengthening process with a simple isometric exercise. Place your palm on the side of your head, just above your ear, fingers pointing up. Press your hand against your head and your head into your hand with equal force, so the side muscles contract but your head doesn't move. Hold for 20 to 30 seconds. Do this a few times each day to prepare these muscles for Triangle.
As you develop better alignment in the pose and gradually increase your endurance, your muscles will get stronger and be able to do their job without complaining. While strength in the side-neck muscles doesn't have a lot of benefit for daily activities, it does help with sideways poses such as Ardha Chandrasana (Half Moon Pose) and Parsvakonasana (Side Angle Pose). What's more, strengthening these muscles will help stabilize your neck in Sirsasana (Headstand).