ANSWER
[tex]x=65.9^o[/tex]
EXPLANATION
We are given a right-angled triangle.
We have that the hypotenuse is 46.
The side opposite the given angle is 42.
The angle given is x.
To solve this, we can use trigonometric ratios SOHCAHTOA.
We will use the SOH part of it:
[tex]\sin (x)\text{ = }\frac{opposite}{hypotenuse}[/tex]
So, we have that:
[tex]\begin{gathered} \sin (x)\text{ = }\frac{42}{46} \\ \sin (x)\text{ = 0.9130 } \\ \text{ Find the sine inverse (sin}^{-1})\text{ of 0.9130 to get x:} \\ x=sin^{-1}(0.9130) \\ x=65.9^o \end{gathered}[/tex]
That is the value of the missing angle x.
