Answer: The required value of x is 19.42 units.
Step-by-step explanation: We are given to find the value of x from the figure.
We can see that
the figure contains a right-angled triangle with one acute angle of measurement 72°.
The lengths of the base and hypotenuse related to this acute angle are 6 units and x units respectively.
Therefore, from trigonometric laws of a right-angled triangle, we have
[tex]\cos 72^\circ=\dfrac{6}{x}\\\\\Rightarrow 0.309=\dfrac{6}{x}\\\\\Rightarrow x=\dfrac{6}{0.309}\\\\\Rightarrow x=19.417.[/tex]
Rounding to nearest hundredth, we get
x = 19.42 units.
Thus, the required value of x is 19.42 units.
