High School

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If [tex]\sin f = \frac{8}{9}[/tex] and the measure of overline YW is 24 units, what is the measure of overline YX?

A. 21 units
B. 24 units
C. 27 units
D. 30 units

Answer :

Final answer:

The measure of overline YX is approximately 21 units.Therefore, the measure of overline YX is approximately 21 units.

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.

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Rewritten by : Barada

Answer:

27 units.

Step-by-step explanation:

Since sin f= 8/9, we know that YW would be the opposite, meaning that it would be 24/YX. Since we know that the formula is 8/9. we can say that it would 24/27, which is equal to 8/9 if you divide each side.