Answer: The measure of XY is 36 units
Step-by-step explanation: Please refer to the picture attached for more details.
Note that no diagram was attached , but am constructing a right angled triangle from the question given so as to make the explanations easier.
This question can be best understood if the trigonometric ratios are briefly highlighted since it has been used in the question. Cos f is given as 4/9. Remember that your trig ratios states among other things that, the cos of an angle is derived as the adjacent divided by the hypotenuse. In other words, the cosine of angle f is given as;
Cos f = Adjacent / Hypotenuse
Cos f = 4/9
This simply shows that, in the right angled triangle the adjacent is 4 (the side that lies between the right angle and the reference angle) and the hypotenuse is 9 (the side that faces the right angle).
From the triangle shown in the attachment, the adjacent is XW while the hypotenuse is XY. Hence, the adjacent is 16 units and the hypotenuse is unknown. Since the measurements given in the question are a ratio of the original dimensions, the relationship can be expressed as follows;
4/9 = 16/XY
Where XY is the unknown side
By cross multiplication, you now arrive at,
4XY = 9 * 16
XY = 144/4
XY = 36
Therefore, XY measures 36 units
