To find the value of [tex]\( b \)[/tex] given that [tex]\(\sin x^{\circ} = \frac{4}{5}\)[/tex], let's follow these steps:
1. Recall that in a right triangle, the sine of an angle [tex]\( x \)[/tex] is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Mathematically, [tex]\(\sin x = \frac{\text{opposite}}{\text{hypotenuse}}\)[/tex].
2. Given [tex]\(\sin x = \frac{4}{5}\)[/tex], we can identify the opposite side as 4 and the hypotenuse as 5.
3. Here, we need to find the value of [tex]\( b \)[/tex], which is the hypotenuse in this right triangle. According to the problem, the hypotenuse is 5.
Therefore, the value of [tex]\( b \)[/tex] is:
[tex]\[ b = 5 \][/tex]
So the correct answer is [tex]\( b = 5 \)[/tex].
