We are told that the tangent of an angle x is equal to 0.9004. In order to solve this equation for x we can use the arctangent function that has this property:
[tex]\tan^{-1}(\tan x)=x[/tex]Then we can apply the arctangent to both sides of our equation:
[tex]\begin{gathered} \tan^{-1}(\tan x)=\tan^{-1}0.9004 \\ x=\tan^{-1}0.9004 \end{gathered}[/tex]So our angle is the arctangent of 0.9004 which can be found using a calculator. However calculators oftenly work with radians and we need to express x in degrees. In order to transform the result from radians to degrees we have to perform the following operation:
[tex]x=\tan^{-1}0.9004\cdot\frac{360}{2\pi}=41.999872^{\circ}[/tex]AnswerWheter we round to the nearesth tenth, hundreth or thousanth the answer is 42°.
