To solve for [tex]\( x \)[/tex] in the equation [tex]\(\cos(20^\circ) = \frac{4}{x}\)[/tex], follow these steps:
1. Understand the given equation:
[tex]\[
\cos(20^\circ) = \frac{4}{x}
\][/tex]
2. Isolate [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], multiply both sides of the equation by [tex]\( x \)[/tex]:
[tex]\[
x \cdot \cos(20^\circ) = 4
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Now, to completely isolate [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(\cos(20^\circ)\)[/tex]:
[tex]\[
x = \frac{4}{\cos(20^\circ)}
\][/tex]
4. Substitute the value of [tex]\(\cos(20^\circ)\)[/tex]:
From the given information, we know that:
[tex]\[
\cos(20^\circ) = 0.9396926207859084
\][/tex]
5. Calculate [tex]\( x \)[/tex]:
Substitute [tex]\(\cos(20^\circ)\)[/tex] into the equation:
[tex]\[
x = \frac{4}{0.9396926207859084} \approx 4.256711089903648
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is approximately:
[tex]\[
x \approx 4.256711089903648
\][/tex]
