Answer: The required value of x is 8.1 units.
Step-by-step explanation: We are given to find the value of x from the figure.
From the figure, we notice that
it is a right-angled triangle with the length of the hypotenuse 10 units and one of the acute angle is of measure 36°.
Now, for the angle with measure 36°, the length of the base is x units and the length of the hypotenuse is 10 units.
Therefore, from the laws of trigonometry, we have
[tex]\cos 36^\circ=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos 36^\circ=\dfrac{x}{10}\\\\\\\Rightarrow x=10\times \cos 36^\circ\\\\\Rightarrow x=10\times 0.8090\\\\\Rightarrow x=8.09\\\\\Rightarrow x=8.1.[/tex]
Thus, the required value of x is 8.1 units.
