Final answer:
Angle Q in the right triangle QRS can be found using the tangent function as tan(Q) = opposite / adjacent which equals 7/18. Calculating this gives an angle of approximately 21.8 degrees, which does not match any of the provided options. This indicates a possible error in the question.
Step-by-step explanation:
To determine the measure of angle Q in the right triangle QRS, we can use trigonometric ratios. Since angle S is 90 degrees and we are given the lengths of side QS (7 cm) and side QR (18 cm), we can use the tangent function, which is opposite over adjacent in a right-angled triangle. Here, angle R would be adjacent to QS and opposite to QR.
The tangent of angle Q is equal to the length of side QS divided by side QR, which is tan(Q) = QS / QR = 7 / 18. Using a calculator to find the angle whose tangent is 7/18, we can determine the measure of angle Q.
After calculating the value, we find that angle Q is approximately 21.8 degrees, which is not one of the provided options. Therefore, the answer could be a typographical error in the question, and we may need additional clarification. Normally, we would find the correct measure using a calculator, and then round it to the nearest degree as per the options given.