Answer:
x=14.4
Step-by-step explanation:
We apply the Sine Rule to solve for x:
#We first determine the acute angles of the larger right angles.
[tex]\frac{a}{Sin \ A}=\frac{b}{Sin \ B}=\frac{c}{Sin \ C}\\\\\frac{30}{Sin \ 90\textdegree}=\frac{24}{Sin \ A\textdegree}\\\\A=53.13\textdegree[/tex]
The smaller right angles shares one acute angle of 53.13°.
Therefore the x can be solved applying the Sine Rule again:
[tex]\frac{x}{Sin \ 53.13\textdegree}=\frac{18}{Sin \ 90\textdegree}\\\\x=14.4[/tex]
Hence, the length of x is 14.4
