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What trigonometric expression can be used to find the value of [tex]\( x \)[/tex]? Replace [tex]\( a \)[/tex] and [tex]\( b \)[/tex] with the correct values.

[tex]\[
\tan(b)
\][/tex]

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
[tex]$\frac{\pi}{0}$[/tex] & & [tex]$0^2$[/tex] & +- & [tex]$=$[/tex] & & & & [tex]$\pi$[/tex] & [tex]$a$[/tex] & [tex]$B$[/tex] & 6 & [tex]$\theta$[/tex] & [tex]$\sin$[/tex] & [tex]$\cos$[/tex] & [tex]$\tan$[/tex] & [tex]$\sin ^{-1}$[/tex] & & [tex]$\tan ^{-1}$[/tex] & [tex]$\overline{0}$[/tex] & \begin{tabular}{l}
[tex]$\longrightarrow$[/tex]
\end{tabular} & [tex]$\vec{a}$[/tex] & & \begin{tabular}{l}
[tex]$\Delta$[/tex]
\end{tabular} \\
\hline
[tex]$\sqrt{0}$[/tex] & [tex]$\sqrt{0}$[/tex] & 4 & - [tex]$x$[/tex] & [tex]$\ \textless \ $[/tex] & [tex]$\ \textgreater \ $[/tex] & 5 & [tex]$\geq$[/tex] & & 4 & [tex]$\mu$[/tex] & [tex]$\theta$[/tex] & [tex]$\varphi$[/tex] & [tex]$\csc$[/tex] & sec & cot & [tex]$\log$[/tex] & [tex]$\log _\pi$[/tex] & In & II & 1 & 2 & [tex]$\sim$[/tex] & [tex]$\bullet$[/tex] \\
\hline
\end{tabular}


Sagot :

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].
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