Final answer:
Using the Law of Cosines, we calculate the measure of angle Q in triangle AQRS given the sides q, r, and s. By substituting the given values into the formula and solving for cos(Q), we can find the angle to the nearest tenth of a degree.
Step-by-step explanation:
To find the measure of ∠Q in triangle AQRS to the nearest tenth of a degree, you can use the Law of Cosines. The formula is c² = a² + b² - 2ab×cos(C), where c is the side opposite angle C, and a and b are the other two sides of the triangle.
Firstly, rearrange the formula to solve for cos(C): cos(C) = (a² + b² - c²) / (2ab). Here, a = q = 1.3 cm, b = s = 7 cm, and c = r = 7.6 cm.
By substituting these values into the formula, we get cos(C) = (1.3² + 7² - 7.6²) / (2 * 1.3 * 7), and then use arccos to find the angle: C = arccos[(1.3² + 7² - 7.6²) / (2 * 1.3 * 7)]. Calculate this on your calculator to get the measure of ∠Q. The closest answer to the options given from calculations will be your answer.