sin 60°
√3/2
The value of sin 60° is approximately 0.866.
To understand how this value is obtained, we can use the definition of sine function in a right triangle. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle divided by the length of the hypotenuse.
In a triangle with angles of 30°-60°-90°, the side opposite the 60° angle has a length of √3 times the length of the shorter leg. The hypotenuse has a length of twice the length of the shorter leg.
By using the definition of sine function, we can calculate:
sin 60° = opposite / hypotenuse
= (√3 x shorter leg) / (2 x shorter leg)
= √3 / 2
= 0.866 (rounded to three decimal places)
Therefore, the value of sin 60° is approximately 0.866.
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