What is the cosine value of a triangle with a 60° angle?

The cosine value of a triangle with a 60° angle is indeed √3/2. This is derived from the definitions of the cosine function in a right triangle. Cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

In the context of a unit circle, which is commonly used in trigonometry, the cosine of an angle corresponds to the x-coordinate of the point on the unit circle at that angle. At 60°, the coordinates are (1/2, √3/2), making the cosine value for 60° equal to 1/2.

However, it's important to note that misunderstandings often occur regarding these values. The cosine function identifies how wide the angle is, influencing how much adjacent side length is relevant compared to the hypotenuse in right triangles or the interpretations from the unit circle, which may vary.

For those using the sine or tangent values instead, confusion can arise, as they correspond to different ratios and angles in the same triangle. It can be helpful to visualize a right triangle with angles of 30°, 60°, and 90°, where the lengths of the sides are commonly known and the ratios can be directly calculated.