Let's find the value of [tex]\( x \)[/tex] for which [tex]\( x = \tan^{-1}\left(\frac{3.1}{5.2}\right) \)[/tex].
1. Understanding the Problem:
- We need to determine the value of an angle [tex]\( x \)[/tex] where [tex]\( \tan(x) = \frac{3.1}{5.2} \)[/tex].
- This involves the use of the inverse tangent (or arctangent) function to find the angle [tex]\( x \)[/tex].
2. Applying the Inverse Tangent Function:
- The inverse tangent function, denoted as [tex]\( \tan^{-1} \)[/tex] or [tex]\( \arctan \)[/tex], helps us find an angle whose tangent is a given value.
- Here, we want [tex]\( x = \tan^{-1}\left(\frac{3.1}{5.2}\right) \)[/tex].
3. Calculating the Angle:
- The computation of the arctangent of [tex]\(\frac{3.1}{5.2}\)[/tex] gives us the value of [tex]\( x \)[/tex] in radians.
- The value of [tex]\( x \)[/tex] in radians is [tex]\( 0.5375866466587464 \)[/tex].
4. Converting Radians to Degrees:
- If we need the angle in degrees, we convert from radians to degrees using the conversion factor [tex]\( \frac{180}{\pi} \)[/tex].
- The computed angle in degrees is [tex]\( 30.80144597613683 \)[/tex].
5. Final Step:
- Hence, the value of [tex]\( x \)[/tex] in radians is approximately [tex]\( 0.5376 \)[/tex].
- The value of [tex]\( x \)[/tex] in degrees is approximately [tex]\( 30.80^\circ \)[/tex].
Therefore, in a triangle where the value of [tex]\( x \)[/tex] is equal to [tex]\(\tan^{-1}\left(\frac{3.1}{5.2}\right)\)[/tex], [tex]\( x \)[/tex] is approximately [tex]\( 0.5376 \)[/tex] radians or [tex]\( 30.80 \)[/tex] degrees.
