Answer:
AI-generated answer
To find the measure of Angle Q, the smallest angle in a triangle with side lengths 4, 5, and 6, we can use the Law of Cosines.
The Law of Cosines states that in a triangle with side lengths a, b, and c, and angle A opposite side a, we have the following equation:
c^2 = a^2 + b^2 - 2ab * cos(A)
In this case, we have side lengths 4, 5, and 6, and we want to find the measure of Angle Q, which is opposite side length 4.
Let's use the Law of Cosines to solve for Angle Q:
4^2 = 5^2 + 6^2 - 2 * 5 * 6 * cos(Q)
16 = 25 + 36 - 60 * cos(Q)
16 = 61 - 60 * cos(Q)
60 * cos(Q) = 61 - 16
60 * cos(Q) = 45
cos(Q) = 45/60
cos(Q) = 0.75
Now, we need to find the inverse cosine (cos^(-1)) of 0.75 to find the measure of Angle Q:
Q = cos^(-1)(0.75)
Using a calculator or a trigonometric table, we find that cos^(-1)(0.75) is approximately 41.41 degrees.
Since we need to round the measure to the nearest whole degree, the measure of Angle Q is approximately 41 degrees.
Therefore, the correct answer is 41°.
Explanation: