Let's solve this step by step.
Step 1: Understand the question
You're given that the cosine of an angle (θ) is 1/2. You need to determine the measure of this acute angle in a right triangle.
Step 2: Review cosine definition for acute angles in a right triangle
Cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse.
Step 3: Relate the given information to known values
The value cos(θ) = 1/2 is a known value for specific angles in standard position. Specifically, it corresponds to angles in the first quadrant where cosine values are positive and where the commonly known acute angles are 30°, 45°, and 60°.
Step 4: Recall the specific cosine values for these angles
The cosine of 30° is [tex]\(\sqrt{3}/2\)[/tex], which is not equal to 1/2.
The cosine of 45° is [tex]\(\sqrt{2}/2\)[/tex], which is not equal to 1/2.
The cosine of 60°, however, is exactly 1/2.
Step 5: Conclude
Because the cosine of 60° is 1/2, and we're given that cos(θ) = 1/2, it follows that θ is 60°.
So, the measure of the acute angle θ is 60°.
