Final answer:
Without additional information about the triangle, we cannot determine the length of AC based solely on the given trigonometric ratios. The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio.
Step-by-step explanation:
The question pertains to finding the length of segment AC in a triangle using trigonometric functions. Given that sin(x) = 0.543, cos(x) = 0.840, and tan(x) = 0.646, we can use these trigonometric ratios to find the length of AC if additional information about the triangle is provided, such as the length of another side or the size of angle x. However, without such information, we cannot determine the length of AC solely based on these trigonometric ratios. To solve for lengths in right triangles, one typically uses the Pythagorean theorem or trigonometric functions when an angle and one side length are known.
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions. Consider the following diagram as a reference for an explanation of these three primary functions. This diagram can be referred to as the sin-cos-tan triangle. We usually define trigonometry with the help of the right-angled triangle.