cos 30°
√3/2
The value of cos 30° is √3/2, which is equal to approximately 0.866.
To find this value, we can use the trigonometric function of cosine, which is defined as the ratio of the adjacent side to the hypotenuse in a right-angled triangle.
For a triangle where one of the angles is 30°, the adjacent side is half the length of the hypotenuse and the opposite side is √3/2 times the length of the adjacent side. Using the Pythagorean theorem, we can find the length of the hypotenuse as follows:
Hypotenuse^2 = Adjacent^2 + Opposite^2
Hypotenuse^2 = (1/2)^2 + (√3/2)^2
Hypotenuse^2 = 1/4 + 3/4
Hypotenuse^2 = 1
Hypotenuse = 1
Therefore, the adjacent side is 1/2 and we can use the cosine function to find the value of cos 30°:
cos 30° = Adjacent/Hypotenuse
cos 30° = 1/2/1
cos 30° = 1/2
Simplifying this expression, we find that:
cos 30° = √3/2
So the value of cos 30° is approximately 0.866.
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