Question #200380

Suppose a man stands in front of a mirror as shown below. His eyes are 1.38 m above the floor and the top of his head is 0.284 m higher. Find the height above the floor of the top of the smallest mirror in which he can see both the top of his head and his feet.

answer to 3 decimal places.


1
Expert's answer
2021-05-31T17:09:01-0400

Answer :_

some points

law of reflection θi=θr\theta _i=\theta_r

diagram must be like this


For the Top of the mirror :-

From the figure , it is obvious that the top of the mirror is equal to GD, which is equal to

GD=GA+AD

Similarly as before we can find the distance GA , where thew triangle AGE and FGE shares the same adjecent side , and have the same angle as before due to law of reflection where the incident angle is equal to the reflected angle , and hence

θi=θr\theta_i=\theta_r

tan(θi)=tan(θr)GAGE=GFGEGA=GFtan(\theta_i)=tan(\theta_r)\\ \frac{GA}{GE}=\frac{GF}{GE}\\ GA=GF

And , from the givens we know that

AF=0.284

=GA+GF

=2GA

=2GF

thus,

GA=0.2842=0.142 mGA=\frac{0.284}{2}=0.142 \ m

thus, height of the top mirror which is equal to GD is

GD=GA+AD

= 0.142+1.38

= 1.522m\boxed{1.522 m} answer


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