To find the value of [tex]\( x \)[/tex], the correct trigonometric expression involves the tangent function. Given the problem where the opposite side is 4 and the adjacent side is 5, we can use the tangent function to find the angle [tex]\( b \)[/tex].
Here, we are using the relationship:
[tex]\[ \tan(b) = \frac{\text{opposite side}}{\text{adjacent side}} \][/tex]
Substituting the given values:
[tex]\[ \tan(b) = \frac{4}{5} \][/tex]
Thus, the correct trigonometric expression is:
[tex]\[ \tan(b) = \frac{4}{5} \][/tex]
Applying this expression, we can determine the value of angle [tex]\( b \)[/tex]. From the initial calculations, the angle [tex]\( b \)[/tex] in radians is approximately [tex]\( 0.6747 \)[/tex] and in degrees is approximately [tex]\( 38.66 \)[/tex].
Therefore, the correct trigonometric expression is:
[tex]\[ \tan\left(0.6747\right) = \frac{4}{5} \][/tex]
or equivalently for simplicity:
[tex]\[ \tan(b) = \frac{4}{5} \][/tex] where [tex]\( b \approx 0.6747 \, \text{radians} \)[/tex] or [tex]\( 38.66^\circ \)[/tex].
