Sure! Let's solve for [tex]\( x \)[/tex] in the equation [tex]\(\tan(x) = \frac{6}{8}\)[/tex].
1. Simplify the fraction:
[tex]\[
\tan(x) = \frac{6}{8} = 0.75
\][/tex]
2. Use the inverse tangent function:
To find the angle [tex]\( x \)[/tex], we use the inverse tangent (also called arctan) function.
[tex]\[
x = \tan^{-1}(0.75)
\][/tex]
3. Find [tex]\( x \)[/tex] in radians:
[tex]\[
x \approx 0.6435011087932844 \text{ radians}
\][/tex]
4. Convert from radians to degrees:
To convert from radians to degrees, we use the conversion factor [tex]\( \frac{180}{\pi} \)[/tex].
[tex]\[
x \approx 0.6435011087932844 \times \frac{180}{\pi} \approx 36.86989764584402 \text{ degrees}
\][/tex]
5. Round [tex]\( x \)[/tex] to the nearest hundredth:
[tex]\[
x \approx 36.87^{\circ}
\][/tex]
Therefore, [tex]\( x \approx 36.87^{\circ} \)[/tex].
