Final answer:
The measure of overline YX is approximately 21 units.Therefore, the measure of overline YX is approximately 21 units.
Step-by-step explanation:
The student's question asks for the measure of line segment YX given that sin f = 8/9, and the measure of line segment YW is 24 units.
To solve for YX, we can use the Pythagorean theorem in a right triangle, where YW would be the opposite side relative to angle f, and YX would be the hypotenuse.
Since the sine of an angle in a right triangle is the opposite side divided by the hypotenuse, sin f = YW/YX, we can set up the equation 8/9 = 24/YX. From here, we solve for YX which gives us YX = 24/(8/9) = 24*(9/8) = 3*27 = 27 units. Thus, the measure of line segment YX is 27 units, making option c correct.
To find the measure of overline YX, we need to use the given information that sin f = 8/9 and overline YW = 24 units. Based on the given information, we can set up a trigonometric equation as follows:
sin f = opposite/hypotenuse 8/9 = overline YX/24
We can solve for overline YX by multiplying both sides of the equation by 24:
overline YX = (8/9) * 24 = 64/3 ≈ 21.33 units.
Therefore, the measure of overline YX is approximately 21 units.