Answer:
(a) 18 centimeters.
(b). 27 centimeters.
Step-by-step explanation:
Please find the attachment and consider the complete question.
A toy marble run has ramps and turnaround points. Each ramp is 41 centimeters long. The turnaround is 2 centimeters wide and flat, and entire toy is 42 centimeters wide, as shown.
(a) How tall is the toy?
(b) You add one ore ramp to the toy. How tall is it now?
(a) We will use Pythagoras theorem to solve for the height, h.
[tex](\frac{h}{2})^2+40^2=41^2[/tex]
[tex]\frac{h^2}{4}+1600=1681\\\\\frac{h^2}{4}+1600-1600=1681-1600[/tex]
[tex]\frac{h^2}{4}=81\\\\h^2=4*81\\\\h^2=324\\\\h=18[/tex]
Therefore, the height of the toy is 18 centimeters.
(b) If we will add one more ramp to the toy, it will fix in the slant part as shown in the attachment.
The height of the new toy would be 18 centimeters plus half of 18 centimeters.
[tex]18+9=27[/tex]
Therefore, the height of the new toy would be 27 centimeters.
