If cos f° = 4/9 and the measure of XW is 16 units, what is the measure of XY

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

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3