Answer:
[tex]x \approx 42.6[/tex]
Step-by-step explanation:
We can solve for x using the trigonometric ratio sine:
[tex]\sin(\theta) = \dfrac{\text{opposite}}{\text{hypotenuse}}[/tex]
From the diagram, we can identify the following side lengths:
- opposite = 44
- hypotenuse = 65
Plugging these into the definition of sine along with the angle x°, whose sine we are evaluating:
[tex]\sin(x\°) = \dfrac{44}{65}[/tex]
From here, we can solve for x by taking the inverse sine (or arcsine) of both sides. Know that sine and inverse sine are inverse functions, and when we operate them upon each other, we simply get the input:
[tex]f^{-1}(f(x)) = x[/tex]
Likewise,
[tex]\sin^{-1}(\sin(x)) = x[/tex]
Applying this to the equation at hand:
[tex]\sin^{-1}(\sin(x\°)) = \sin^{-1}\!\!\left(\dfrac{44}{65}\right)[/tex]
[tex]x\° = \sin^{-1}\!\!\left(\dfrac{44}{65}\right)[/tex]
Finally, we can evaluate the right side by plugging it into a calculator. Make sure the calculator setting is set to DEGREES.
[tex]x\° \approx 42.6\°[/tex]
[tex]\boxed{x \approx 42.6}[/tex]
