Answer:
[tex]x\approx 67.5\°[/tex]
Step-by-step explanation:
We can solve for x using the trigonometric ratio tangent:
[tex]\tan(\theta) = \dfrac{\text{opposite}}{\text{adjacent}}[/tex]
where:
- [tex]\theta[/tex] is the interior angle of a right triangle.
Since x is supplementary to its adjacent interior angle ([tex]\theta[/tex]), we can say that:
[tex]x + \theta = 90\°[/tex]
Rearranging the equation to solve for [tex]\theta[/tex], we get:
[tex]\theta = 90\° - x[/tex]
Now, we can plug the known values into the tangent equation:
[tex]\tan(90\° - x) = \dfrac{3.4}{8.2}[/tex]
↓ taking the inverse tangent of both sides
[tex]90\°-x=\tan^{\!-1}\!\left(\dfrac{3.4}{8.2}\right)[/tex]
↓ rearranging to isolate x on one side
[tex]x=90\°-\tan^{\!-1}\!\left(\dfrac{3.4}{8.2}\right)[/tex]
↓ evaluating using a calculator
[tex]x\approx 67.4794\°[/tex]
Finally, we can round to 1 decimal place (tenths place):
[tex]\boxed{x\approx 67.5\°}[/tex]
