Answer: In general, if you know the diagonal and the angle of depression of a rectangular mirror, you can use trigonometric functions to find the length and width of the mirror. However, whether to use sine or cosine to find the length or width depends on the angle you are given.
In the case of the problem you mentioned, the angle given is the angle of depression, which is the angle between the horizontal line and the line of sight to the bottom of the mirror. The sine function is used to find the length of the mirror because the length is opposite to the angle of depression, while the cosine function is used to find the width of the mirror because the width is adjacent to the angle of depression.
However, if the angle given is the angle of elevation (the angle between the horizontal line and the line of sight to the top of the mirror), then you would use cosine to find the length and sine to find the width.
So, in summary, the trigonometric function to use depends on the given angle, and it is important to understand the relationship between the angle and the sides of the right triangle in order to correctly apply the trigonometric function.