To solve the problem, we begin with the given information that [tex]\(\sin x^{\circ} = \frac{4}{5}\)[/tex].
Recall that for a right-angled triangle, the sine of an angle [tex]\(x\)[/tex] is given by the ratio of the length of the opposite side to the hypotenuse:
[tex]\[
\sin x = \frac{\text{opposite}}{\text{hypotenuse}}
\][/tex]
Given that [tex]\(\sin x^{\circ} = \frac{4}{5}\)[/tex], we can identify the following:
- The opposite side to angle [tex]\(x\)[/tex] is 4.
- The hypotenuse of the triangle is 5.
From this, it is clear that the values corresponding to the sides are:
- Opposite side = 4
- Hypotenuse = 5
Therefore, the value of [tex]\(b\)[/tex] that fits this context (from the given choices) is:
[tex]\[
b=4
\][/tex]
[tex]\[
b=5
\][/tex]
[tex]\[
b=6
\][/tex]
[tex]\[
b=7
\][/tex]
Comparing with the choices provided, the correct value of [tex]\(b\)[/tex] when [tex]\(\sin x^{\circ} = \frac{4}{5}\)[/tex] is:
[tex]\[
b = 5
\][/tex]
