Question

If sin f° = eight ninths and the measure of segment YW is 24 units, what is the measure of segment YX? (4 points)

triangle XYW in which angle W is a right angle, angle X measure f degrees, and angle Y measures d degrees

21 units

24 units

27 units

30 units

Answer 1

To find the measure of segment \( YX \) given that \( \sin f^\circ = \frac{8}{9} \) and the measure of segment \( YW = 24 \) units, we can use the definition of the sine function in a right triangle.

In triangle \( XYW \), where angle \( W \) is the right angle, we have:

- \( YW \) is the side opposite angle \( X \),
- \( YX \) is the hypotenuse,
- and \( XY \) is the side adjacent to angle \( X \).

Given:
- \( YW = 24 \) units,
- \( \sin f^\circ = \frac{8}{9} \).

From the definition of sine:
\[
\sin f^\circ = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{YW}{YX}
\]
Substituting the known values:
\[
\frac{8}{9} = \frac{24}{YX}
\]

To solve for \( YX \), we can cross-multiply:
\[
8 \cdot YX = 9 \cdot 24
\]
\[
8 \cdot YX = 216
\]
Now, divide both sides by 8:
\[
YX = \frac{216}{8} = 27
\]

Thus, the measure of segment \( YX \) is **27 units**.

The answer is:
**27 units**