Answer:
[tex]70^\circ, 250^\circ[/tex]
Step-by-step explanation:
Given that:
[tex]tan x= 2.7475[/tex]
and [tex]0^\circ < x < 360^\circ[/tex] i.e. [tex]x[/tex] lies in the interval [tex]0^\circ[/tex] to [tex]360^\circ[/tex] or [tex]0\ to\ 2\pi[/tex].
To find: The possible values for x in the interval [tex]0^\circ[/tex] to [tex]360^\circ[/tex] = ?
First of all, let us learn something about [tex]tan\theta[/tex].
In a right angled triangle the value of [tex]tan\theta[/tex] can be calculated as follows:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
i.e. [tex]tan\theta[/tex] is equal to the ratio of Perpendicular to Base in a right angled triangle.
We are given that:
[tex]tan x= 2.7475[/tex]
[tex]\Rightarrow x = tan^{-1}(2.7475)\\\Rightarrow x = 70^\circ[/tex]
So, the value of x in first quadrant is [tex]70^\circ[/tex].
It is also known that value of tangent is positive in the first and third quadrant.
We are given a positive value of tangent here,
So, another value of [tex]x = 180^\circ+70^\circ = 250^\circ[/tex]
Hence, the correct answers are: [tex]x=70^\circ, 250^\circ[/tex]
