Certainly! Let's solve the given problem step by step.
We start with the equation:
[tex]\[ 53 \tan \theta = 12 \][/tex]
1. Isolate [tex]\(\tan \theta\)[/tex]:
[tex]\[
\tan \theta = \frac{12}{53}
\][/tex]
2. Calculate the value of [tex]\(\frac{12}{53}\)[/tex]:
[tex]\[
\tan \theta \approx 0.2264
\][/tex]
3. Find the angle [tex]\(\theta\)[/tex] in radians:
To find the angle [tex]\(\theta\)[/tex], we use the [tex]\(\tan^{-1}\)[/tex] (arctan) function.
[tex]\[
\theta = \tan^{-1}(0.2264) \approx 0.2227 \text{ radians}
\][/tex]
4. Convert the angle from radians to degrees:
We use the conversion factor [tex]\(180^\circ / \pi\)[/tex] to convert from radians to degrees.
[tex]\[
\theta \approx 0.2227 \times \frac{180}{\pi} \approx 12.76^\circ
\][/tex]
5. Round the answer to 1 decimal place:
[tex]\[
\theta \approx 12.8^\circ
\][/tex]
Therefore, the value of [tex]\(\theta\)[/tex] rounded to one decimal place is [tex]\(12.8^\circ\)[/tex].
