Answer: The correct option is (A) 0.75.
Step-by-step explanation: Given that the two right-angled triangles in the figure are similar. We are to find the ratio of the height to the base for the triangles.
In the first triangle,
height, h = 6 units and base, b = 8 units,
In the second triangles,
height, h' = 3 units and base, b' = 4 units.
Since the two triangles are similar, so the corresponding sides will be proportional.
We can see that
[tex]\dfrac{h}{h'}=\dfrac{b}{b'}=\dfrac{6}{8}=\dfrac{3}{4}=0.75.[/tex]
Hence, we can write
[tex]\dfrac{h}{b}=\dfrac{h'}{b'}=0.75[/tex]
Therefore, the ratio of the height to the base of the triangles is 0.75.
Thus, (A) is the correct option.
