From the given sentence, identify the highlighted word that is either incorrectly spelled or used in an inappropriate context.

Because she could not endure the intollerable racket of the broken engine, she had no choice but to request the assistance of an emergency repair professional.

The correct option is intollerable.

Let's analyze the highlighted words in the given sentence step-by-step:

1. intollerable: This word is misspelled. The correct spelling is intolerable (with a single 'l'), which means unable to be resisted or endured.

2. racket: Used correctly to refer to a loud, unpleasant noise.

3. emergency: Used correctly as an adjective describing a serious, unexpected situation requiring immediate action.

4. professional: Used correctly to refer to a person engaged in a specified activity as one's main paid occupation.

Therefore, intollerable is the word that is incorrectly spelled in the given context.