To solve for [tex]\( x \)[/tex] given that [tex]\(\tan(x) = \frac{6}{8}\)[/tex], follow these steps:
1. Identify the given ratio:
We are given [tex]\(\tan(x) = \frac{6}{8}\)[/tex]. Simplify the ratio:
[tex]\[
\frac{6}{8} = 0.75
\][/tex]
2. Find the angle using the inverse tangent function:
Use the inverse tangent function [tex]\(\tan^{-1} (0.75)\)[/tex] to find [tex]\( x \)[/tex]:
[tex]\[
x = \tan^{-1}(0.75)
\][/tex]
3. Convert the calculated angle from radians to degrees:
The output of [tex]\(\tan^{-1}\)[/tex] is typically in radians. To convert this value to degrees, use the conversion factor [tex]\(\frac{180}{\pi}\)[/tex] degrees per radian.
4. Perform the calculation (in degrees):
Calculating [tex]\(\tan^{-1}(0.75)\)[/tex] yields approximately [tex]\( 0.6435011087932844 \)[/tex] radians. Converting this to degrees:
[tex]\[
x = 0.6435011087932844 \times \frac{180}{\pi} \approx 36.86989764584402 \text{ degrees}
\][/tex]
5. Round to the nearest hundredth:
Finally, round [tex]\(36.86989764584402\)[/tex] degrees to the nearest hundredth:
[tex]\[
x \approx 36.87 \text{ degrees}
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is approximately:
[tex]\[
x \approx 36.87 \text{ degrees}
\][/tex]
