Final answer:
To find the values of sine, cosine, and tangent for angle ZA, we look for the option with proper trigonometric ratios. Option a) sin ZA = 11/157, cos ZA = 6/157, and tan ZA = 11/6 is the correct one, as it adheres to the range for sine and cosine values and the Pythagorean identity.
Step-by-step explanation:
The question asks to find the values of the sine, cosine, and tangent for an angle ZA. These trigonometric functions are based on the ratios of sides in a right triangle. The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse, the cosine is the ratio of the length of the adjacent side to the hypotenuse, and the tangent is the ratio of the sine to the cosine or the opposite over the adjacent.
Given the options presented and recognizing that the sine and cosine values must be between -1 and 1 (since they are ratios of sides of a triangle), we can eliminate the options where sine and cosine are greater than 1 or less than -1. This rules out options c) and d). Also, if the cosine value is 6/157, then the sine cannot also be 6/157 due to the Pythagorean identity (sin^2 + cos^2 = 1). This eliminates option b) as well, leaving us with option a) sin ZA = 11/157, cos ZA = 6/157, tan ZA = 11/6, which is the set of trigonometric ratios that fits the parameters of the problem.