What is the measure of x to the nearest degree?
8

We know that :
[tex]\sf{\bigstar \ \ Cos\theta = \dfrac{Adjacent \ Side}{Hypotenuse}}[/tex]
From the figure, We can notice that :
Ф Adjacent side length = 8
Ф Hypotenuse length = 11
[tex]\sf{\implies Cosx^{\circ} = \dfrac{8}{11}}[/tex]
[tex]\sf{\implies x^{\circ} = Cos^{-1}\bigg(\dfrac{8}{11}\bigg)}[/tex]
[tex]\sf{\implies x^{\circ} = 43.34}[/tex]