To solve the equation
[tex]\[
\sin 30^{\circ} = \frac{x}{6}
\][/tex]
we will follow these steps:
1. Identify the sine value of [tex]\(30^\circ\)[/tex]:
The sine of [tex]\(30^\circ\)[/tex] is well known from trigonometric tables. It is:
[tex]\[
\sin 30^\circ = 0.5
\][/tex]
2. Substitute [tex]\(\sin 30^\circ\)[/tex] with its value:
Replace [tex]\(\sin 30^\circ\)[/tex] in the original equation with 0.5. The equation becomes:
[tex]\[
0.5 = \frac{x}{6}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex] in the equation [tex]\(0.5 = \frac{x}{6}\)[/tex], multiply both sides by 6:
[tex]\[
0.5 \times 6 = x
\][/tex]
4. Calculate the value of [tex]\(x\)[/tex]:
Perform the multiplication:
[tex]\[
0.5 \times 6 = 3
\][/tex]
Therefore,
[tex]\[
x = 3
\][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation
[tex]\[
\sin 30^\circ = \frac{x}{6}
\][/tex]
is [tex]\(x = 3\)[/tex].
