Final answer:
Insulin should be administered to a frail, older client at a 45 degrees angle to ensure that the medication is deposited into the subcutaneous tissue. This angle helps avoid injection into muscle and is suited for clients with limited adipose tissue.
Step-by-step explanation:
When administering insulin to a frail, older client with a failure to thrive, the angle of needle insertion is essential to ensure correct delivery of the medication and reduce the risk of injury. In general, for clients who are thin, including those who are frail and have failure to thrive, insulin injections should be administered at a 45 degrees angle to prevent injection into muscle, which can alter the absorption rate of the insulin. Therefore, the correct answer to the question is c. 45 degrees.
For a subcutaneous injection, where there is limited adipose tissue, the shorter needle length and a 45-degree angle help in depositing the insulin into the subcutaneous fat rather than deeper tissues. A 90 degrees angle is typically used for clients with more adipose tissue. Angles less than 45 degrees, such as 10-15 degrees and 20-30 degrees, are not common for insulin injections and could be used for intradermal injections, where a shallow angle is required.