In ΔQRS, q = 9 inches, r = 1.7 inches and s=9.4 inches. Find the measure of ∠Q to the nearest degree.

To find the measure of ∠Q in ΔQRS, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of lengths a, b, and c and an angle γ opposite the side of length c, the following relationship holds:

c² = a² + b² - 2ab cos(γ)

In this case, we know the lengths of all three sides (q = 9 inches, r = 1.7 inches, and s = 9.4 inches), and we want to find the measure of ∠Q, which is opposite the side of length q. So we can set up the equation as follows:

q² = r² + s² - 2rs cos(Q)

Substituting the given values, we get:

9² = 1.7² + 9.4² - 21.79.4 cos(Q)

Solving for cos(Q), we get:

cos(Q) = (1.7² + 9.4² - 9²) / (21.79.4)

Now, we can use a calculator to find the numerical value of cos(Q).

Finally, to find the measure of ∠Q, we take the arccos (inverse cosine) of the value we found for cos(Q).

Remember to convert the result from radians to degrees if your calculator is set to give the result in radians.

Round your answer to the nearest degree.