Answer: The value of x is 57.8.
Step-by-step explanation: We are given to find the value of x to the nearest tenth.
We can see from the figure that
the triangle is a right-angled triangle with one of the legs measuring 11 units and the hypotenuse is 13 units in length.
For the acute angle measuring x°, the perpendicular measures 11 units.
So, we get
[tex]\sin x^\circ=\dfrac{perpendicular}{hypotenuse}\\\\\\\Rightarrow \sin x^\circ=\dfrac{11}{13}\\\\\\\Rightarrow \sin x^\circ=0.8461\\\\\Rightarrow x^\circ=\sin^{-1}{0.8461}\\\\\Rightarrow x^\circ=57.7899\\\\\Rightarrow x^\circ=57.8^\circ\\\\\Rightarrow x=57.8.[/tex]
Thus, the value of x is 57.8.
