We have two triangles with the same angles, then, they're are proportional to each other.
By the pythagorean theorem we can find the missing side of the smallest triangle:
pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]Where 'c' represents the hypotenuse, and 'a' and 'b' represent the other two sides. Applying this theorem in the smallest triangle we have the following relation:
[tex]3^2+b^2=5^2\text{ }\Rightarrow\text{ b = 4}[/tex]Now that we have our missing side, we can compare the smallest triangle with the biggest triangle.
The ration between 4 and 8 is the same of the hypotenuses of both triangles( x and 5)
Then, we have the following equation:
[tex]\frac{4}{8}=\frac{5}{x}\Rightarrow\text{ 4 }\times\text{ x = 5 }\times\text{ 8}[/tex]Just solving this equation, we get the following result
[tex]\begin{gathered} x\text{ = }\frac{40}{4}\text{ } \\ x\text{ = 10} \end{gathered}[/tex]