Answer:
[tex]\mathrm{A.\: 39.3}[/tex]
Step-by-step explanation:
Let [tex]h[/tex] represent the height of the two smaller triangles in this figure. Because all three triangles are similar, we can set up the following proportion:
[tex]\frac{33}{h}=\frac{h}{y}[/tex], for [tex]y=x-33[/tex].
We can solve for [tex]h[/tex] using the Pythagorean theorem on the second largest triangle:
[tex]33^2+h^2=36^2,\\h=\sqrt{36^2-33^2},\\h=\sqrt{207}[/tex].
Now plugging in [tex]h=\sqrt{207}[/tex] into our proportion [tex]\frac{33}{h}=\frac{h}{y}[/tex], we can solve for y:[tex]\frac{33}{\sqrt{207}}=\frac{\sqrt{207}}{y}[/tex].
Cross-multiply to get:
[tex]33y=207,\\y=\frac{207}{33},\\y\approx 6.3[/tex].
Since we [tex]y=x-33, y+33=x[/tex].
Therefore, our answer is:
[tex]x=33+y=33+6.3=\fbox{$\mathrm{A.\: 39.3}$}[/tex].
