Final answer:
The length of side YZ can be calculated using the sine function. Sin(16°) multiplied by the hypotenuse (7 units) results in approximately 1.932 units, which does not match the answer choices provided.
Step-by-step explanation:
In right triangle XYZ, where angle Z is a right angle, we know that angle Y is 16 degrees and the length of hypotenuse XY is 7 units. To find the length of side YZ, we can use the sine function, since sine is defined as the opposite side over the hypotenuse in a right triangle. In this case, the sine of angle Y will give us the length of side YZ divided by the hypotenuse XY.
The formula is as follows:
sin(Y) = YZ/XY
Plugging in the values we know:
sin(16°) = YZ/7
To solve for YZ, we multiply both sides by 7:
YZ = 7 * sin(16°)
Using a calculator, sin(16°) ≈ 0.276.
Therefore:
YZ = 7 * 0.276
YZ = 1.932
After calculating, we see that none of the answer choices (a) through (d) match our result. It seems there might be a mistake in the provided answer choices or the question might have some typos. Usually, for mistakes or uncertainties, it is best to communicate with the student and clarify the discrepancy.