Answer:
The distance between library and museum is 400 yards.
Step-by-step explanation:
Let L represents the position of library, R represents the restaurant and M represents the museum,
Since, By the given diagram,
∠MLR = 90°,
LR = 300 yd,
RM = 500 yd,
So, by the Pythagoras theorem,
[tex]RM^2=LR^2+ML^2[/tex]
[tex]\implies ML^2=RM^2-LR^2[/tex]
[tex]\implies ML=\sqrt{RM^2-LR^2}[/tex]
By substituting the values,
[tex]ML = \sqrt{500^2-300^2}[/tex]
[tex]=\sqrt{250000-90000}[/tex]
[tex]=\sqrt{160000}[/tex]
[tex]=400[/tex]
Hence, the distance between library and museum is 400 yards.
