This question is asking about the value of the angle that gives us a sine of 4/15.
To find this angle, we need to use the inverse function of the sine function which is called arcsin function, and it is also represented as:
[tex]\arcsin (x)=\sin ^{-1}(x)[/tex]
Then, to find the angle, we need to apply the latter function on both sides of the equation as follows:
[tex]\arcsin (\sin (x^{\circ}))=\arcsin (\frac{4}{15})=\sin ^{-1}(\frac{4}{15})=15.4660099534[/tex]
We need to be careful that the value that gives us a calculator is in degrees (as in this case).
If we round the answer to the nearest tenth, we finally have that:
[tex]\arcsin (\sin (x^{\circ})=x^{\circ}=15.5[/tex]
In summary, the value for angle x° is equal to 15.5° (third option).
