Solve for [tex][tex]$x$[/tex][/tex].

[tex]\[
\tan (x)=\frac{6}{8}
\][/tex]

[tex]\[ x = [?]^{\circ} \][/tex]

Hint: Use the inverse tangent function [tex]\(\left(\tan^{-1}\left(\frac{6}{8}\right)\right)\)[/tex].

Round to the nearest hundredth.



Answer :

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].