Step 1: Translate the symptom into a physiological need.
The singer cannot raise her pitch, and the cords are seen depressed and bowed (lax, not taut). Pitch rises when the vocal folds are made longer, thinner and more tense; so the failing structure must be the one that lengthens and tightens the cords.
Step 2: Recall the mechanics of pitch control.
Tension of the vocal folds is set chiefly by tilting the thyroid cartilage forward on the cricoid. This forward tilt stretches the cords, increasing their length and tension - the physical basis of a higher note. The muscle that produces this tilt is the cricothyroid.
Step 3: Note the nerve angle.
The cricothyroid is the only intrinsic laryngeal muscle supplied by the external branch of the superior laryngeal nerve (all others run with the recurrent laryngeal nerve). Its weakness gives exactly this picture - an inability to reach high pitch with bowed, lax cords.
Step 4: Show the other muscles can't explain it.
• Interarytenoid: an adductor that closes the back of the glottis - governs closure, not tension/pitch.
• Posterior cricoarytenoid: the sole abductor, opens the glottis for breathing - not a tensor.
• Lateral cricoarytenoid: an adductor that closes the glottis - again concerned with approximation, not tightening.
None of these stretch the cords, so none can be the cause of lost high pitch.
Final answer: The muscle involved is Option 1 - the cricothyroid.