Hello!
The answer is:
The value of "x" is 90.16
Why?
To solve the problem we need to use the trigonometric identity of the sine that establish that:
[tex]Sin(\alpha )=\frac{OppositeSide}{Hypotenuse}[/tex]
So, we are given the following information:
[tex]\alpha =48(degrees)\\\\OppositeSide=67[/tex]
Then, applying the trigonometric identity, we have:
[tex]Sin(48)=\frac{67}{Hypotenuse}[/tex]
[tex]Sin(48)=\frac{67}{Hypotenuse}\\\\Hypotenuse=\frac{67}{sin(48)}=90.157=90.16[/tex]
Hence, the value of "x" is (rounded to the nearest hundreth) 90.16.
Have a nice day!
