What is the value of cos 30°?

The value of cos 30° is 0.866, which is derived from the properties of a 30-60-90 triangle. In such a triangle, the ratios of the lengths of the sides are well-known: the side opposite the 30° angle is half the length of the hypotenuse, while the side opposite the 60° angle is equal to the square root of 3 times the length of the shorter side.

When calculating cosine, which represents the adjacent side over the hypotenuse, for a 30° angle, we find that:

• The length of the hypotenuse can be treated as 1 (a convenient choice for simplicity).
• The adjacent side (along the 60° angle) will then be the square root of 3 divided by 2, and since this corresponds to the cosine of 30°, we arrive at cos 30° = sqrt(3)/2.

The decimal approximation of sqrt(3) is about 1.732, which when divided by 2 gives approximately 0.866. This confirms that the value of cos 30° is indeed 0.866.

The other values given do not represent the correct cosine of 30°. The option