The inquiry letter is useful when you need information, advice, names, or directions. Be careful, however, not to ask for too much information or for information that you could easily obtain in some other way, for example, by a quick trip to the library.
Inquiry letters relate to the language function of making requests, usually making requests of information.
Inquiry Letters: Types and Contexts
There are two types of inquiry letters: solicited and unsolicited. You write a solicited letter of inquiry when a business or agency advertises its products or services. For example, if a software manufacturer advertises some new package it has developed and you can't inspect it locally, write a solicited letter to that manufacturer asking specific questions. Your letter of inquiry is unsolicited if the recipient has done nothing to prompt your inquiry. For example, if you read an article by an expert, you may have further questions or want more information. You must construct the unsolicited type more carefully, because recipients of unsolicited letters of inquiry are not ordinarily prepared to handle such inquiries.
Inquiry Letters: Contents and Organization Early in the letter, identify the purpose - to obtain help or information (if it's a solicited letter, information about an advertised product, service, or program).
If relevant (mostly unsolicited letters), give to-the-point information related to your purpose: who you are, what you are working on, and why you need the requested information, and how you found out about the individual.
In the letter, list questions or information needed in a clear, specific, and easy-to-read format. If you have quite a number of questions, consider making a questionnaire and including a stamped, self-addressed envelope.
In a solicited letter, suggest that the recipient send brochures or catalogs. In an unsolicited letter, try to find some way to compensate the recipient for the trouble, for example, by offering to pay copying and mailing costs, to accept a collect call, to acknowledge the recipient in your report, or to send him or her a copy of your report.
In closing an unsolicited letter, express gratitude for any help that the recipient can provide you, acknowledge the inconvenience of your request, but do not thank the recipient "in advance." In an unsolicited letter, tactfully suggest to the recipient will benefit by helping you (for example, through future purchases from the recipient's company).
From the site
Online Technical Writing, an example of an unsolicited inquiry letter and one of a solicited inquiry letter
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