To find the value of [tex]\( x \)[/tex] using the given trigonometric expression for a right triangle where [tex]\( a \)[/tex] is the length of the side adjacent to the angle [tex]\( b \)[/tex]:
1. The trigonometric expression we need to use is:
[tex]\[
x = \frac{a}{\tan(b)}
\][/tex]
2. We are given specific values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
- [tex]\( a = 5 \)[/tex] (the length of the adjacent side)
- [tex]\( b = 30^\circ \)[/tex] (the measure of the angle in degrees)
3. Substitute these values into the trigonometric expression:
[tex]\[
x = \frac{5}{\tan(30^\circ)}
\][/tex]
4. Recall that [tex]\( \tan(30^\circ) \)[/tex] is a known value in trigonometry. Specifically:
[tex]\[
\tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.57735
\][/tex]
5. Therefore, substituting this into the equation gives us:
[tex]\[
x = \frac{5}{0.57735}
\][/tex]
6. Performing the division:
[tex]\[
x \approx 8.660254037844387
\][/tex]
Thus, the value of [tex]\( x \)[/tex] using the given trigonometric expression with the provided values is approximately [tex]\( 8.660254037844387 \)[/tex].
